computer programma's (2022)
______________________________________
computer programma's ( build 2015,update 05/06/2015)
1e :Van Der Waals vergelijking (equation of state of thermodynamics)
Welke oplossing vindt het computer programma :
numerical method : Newton Raphson (oplossing van nonlinear equations)
nonlinear equations :f(v)=v^3-(b+q)*v^2+a/p*v-a*b/p
eerste oplossing : start waarde ( v=b)
a) saturated liquid volume ( m^3/mol)
tweede oplossing : start waarde ( v=q=r*t/p)
b) saturated vapour volume (m^3/mol)
download code :
programma van der waals
output view : (video,*.png)
view van der waals
2e:Proces material balances:( example :binairy distillation of alcohol,water)
info :staat tussen de code zoals weergegeven op de startpagina.
numerical method : Method van Cramer (oplossing van linear equations)
linear equations : b=A*x (b,x='kolom vector', A=' Matrix')
download code :
programma processmatfinal
output view : (video,*.png)
view processmatfinal
3e:Proces material balances:( doublebindist =>first (unit) naar de sec(unit))
info :staat tussen de code zoals weergegeven op de startpagina.
numerical method : Method of Cramer (oplossing van linear equations)
linear equations : b=A*x
download code :
programma doublebindist
output view : (video,*.png)
view doublebindist
4e:Dewpoint calculation (nl:dauwpunt)
info :staat tussen de code zoals weergegeven op de startpagina.
numerical method : Newton Raphson (oplossing van nonlinear equations)
nonlinear equation :f(T)=1/p-y1*exp(a1-b1/(T+c1))-y2*exp(a2--b2/(T+c2))
downloadcode:
program dewpoint
output view : (video,*.png)
view dewpoint
5e:Bubblepoint calculation (nl:kookpunt)
info :staat tussen de code zoals weergegeven op de startpagina.
numerical method : Newton Raphson (oplossing van nonlinear equations)
nonlinear equation:f(T)=p-x1*exp(a1-b1/(T+c1))-x2*exp(a2--b2/(T+c2))
download code:
programma bubblepoint
output view:
view bubblepoint
6e:Antoine equation (solution)
info:staat tussen de code zoals weergegeven op de startpagina.
Welke oplossing vindt het computer programma.
download code:
Antoineeq
eerste oplossing: calculation vapour pressure ( given : temperature )
output view:
view Antoineeqvap
tweede oplossing: calculation temperature ( given : vapour pressure)
output view:
view Antoineeqtemp
sub routines : 1e) sort (kan gebruikt worden voor sorteren van wortels van een polynoom)
download code : sortswap
output view : view sortswap
2e) gauss-seidel (solving b=A*x,iteration procedure, start gegeven kolom vector x)
download code: gauss-seidel
output view :view gauss-seidel
example : mat(A) =a(i,j) i=1..n,j=1..m ,n<>m (Matrix A :nl)
det(A) = number (A=a(n,n), determinant van A met resultaat een getal:nl)
truebasic syntax: det,mat,mat print ... (compiler=truebasic)
option nolet
!****************************************************
! sub routine -> "doubledistil1gauss-seidel "
!****************************************************
print "---------------------------------------------"
print " algo gauss-seidel: (linear equations) => "
print " [email protected] "
print " sub :gauss-seidel ,27-05-2015 "
print "---------------------------------------------"
print " gauss-seidel method (solve lin_equations) "
!**************************************************
dim x_n(1),x_o(1),v(1),check(1)
! number of variables n=3
! -> [ x(1),x(2),x(3)]
mat redim x_n(3),x_o(3),v(3),check(3)
!**************************************************
!--------------------------------------------------
!**************************************************
print " system: "
print "*************************"
print "10*x(1)+x(2)+2*x(3)=44 "
print "2*x(1)+10*x(2)+x(3)=51 "
print "1*x(1)+2*x(2)+10*x(3)=61 "
print "*************************"
!*****************************
! solve (system,x(i))
!*****************************
!-----------------------------
!*************************************************
print "start values for iteration for x(i) i=1..3"
!*************************************************
x_n(1)=2.0
x_n(2)=3.0
x_n(3)=4.0
mat print x_n
do
x_o(1)=x_n(1)
x_o(2)=x_n(2)
x_o(3)=x_n(3)
x_n(1)=(44.0-x_o(2)-2*x_o(3))/10
x_n(2)=(51.0-2*x_n(1)-x_o(3))/10
x_n(3)=(61.0-x_n(1)-2*x_n(2))/10
for i=1 to 3
v(i)=abs(x_n(i)-x_o(i))
next i
loop until ( v(1)< 1e-7 and v(2)< 1e-7 and v(3)< 1e-7)
!**************************************
print "solution of system -> x(i) i=1..3 "
!**************************************
mat print x_n
!**************************************
!check lin_equations
!**************************************
print " sum of each row in the system :check "
!**************************************
check(1)=10*x_n(1)+x_n(2)+2*x_n(3)
check(2)=2*x_n(1)+10*x_n(2)+x_n(3)
check(3)=1*x_n(1)+2*x_n(2)+10*x_n(3)
!**************************************
mat print check
end
computer programming(TrueBasic,Maxima (2022)
_____________________________________________________________
'NEW 2017 - 2022'
Programming :'TrueBasic',True BASIC Bronze Edition v.6 Demo
======================================================
new: 15/05/2018 :Correction, modification, TBdemos
outp : run the file
rem : orginal
download (TrueBasic,code):AREAS
rem : modification
download (TrueBasic,code): REASmod AREASmod
download (TrueBasic,code):AREASmoderrorcatch,(problem with upload)
rem : LIBRARY "BronzeTD.trc"
download (TrueBasic,lib):BronzeTD.trc
new: 15/05/2018 :elek1:interactive Ohms Law
download (TrueBasic,code):Ohmslawinteractiverversion1
download (TrueBasic,outp) :Ohmslawinteractiverversion1outp
new: 28/05/2018 :elek2:Electrical networks : Ohms Law,Kirchoff Current Law.
modification version without line numbers: from John G.K,Thomas E.K
download (TrueBasic,code):elek2electricalnetworksfinalversion1
download (TrueBasic,outp) :elek2electricalnetworksfinalversion1outp
new: 16/05/2018 :cursor,example,version 1.0'
download (TrueBasic,code):cursormoveexample
download (TrueBasic,outp):cursormoveexampleoutp
new: 16/05/2018 :factorial 'error control'
download (TrueBasic,code):factorialerrorcatchsub
download (TrueBasic,outp):factorialerrorcatchsuboutp
new: 31/03/2019 :fibonacci list
download (TrueBasic,code):fibadvanced
download (TrueBasic,outp):fibadvancedoutp
new: 22/01/2020 :programming :truebasic, random_walk 'version 1'
rem : see Maxima Programming
download (TrueBasic,code):TRUERADOMWALKVERSION1
download (TrueBasic,outp):TRUERADOMWALKVERSION1outp
download (info example,pdf):TRUERADOMWALKVERSION1pdf
new: 01/22/2020 :programming :truebasic, bet game play ,'version 1.0',problem 2
! < roll the dice : >
! main program
option nolet
randomize
x=0
do while x < 100
call roll_dice(roll)
x=x+1
print " roll= ";roll
loop
end
! sub roll dice => argument : roll
sub roll_dice(roll)
roll = int(6*rnd)+1
end sub
download (TrueBasic,code):rolldiceproblem2
download (TrueBasic,outp):rolldiceproblem2outp
new:22/01/2020 :programming :truebasic, bet game play(monte carlo:simulation),'version 1.0'
rem : see Monte Carlo method
download (TrueBasic,code):ROLLDICEPROBLEM3montecarlosimulation
download (TrueBasic,outp):ROLLDICEPROBLEM3montecarlosimulationoutp
new: 01/02/2020 :programming :truebasic, random_walk (begin,end), 'version 1.0a'
download (TrueBasic,code):TRUERADOMWALKVERSION1GIVENBEGINEND3
download (TrueBasic,outp):TRUERADOMWALKVERSION1GIVENBEGINEND3outp
download (TrueBasic,code):TRUERADOMWALKVERSION1GIVENBEGINEND4
download (TrueBasic,outp):TRUERADOMWALKVERSION1GIVENBEGINEND4outp
new: 13/02/2020 :programming :truebasic, recursion: Ackermann function,version 1.0
download (TrueBasic,code):TRUEACKERMANNFUNCTIONVERSION1FINALfinal
download (TrueBasic,outp):TRUEACKERMANNFUNCTIONVERSION1FINALfinaloutp
new: 26/02/2020 :programming :truebasic, tree example ,version 1.0
download (TrueBasic,code):TREEEXAMPLETRUEBVERSION1FINALFINAL
download (TrueBasic,outp):TREEEXAMPLETRUEBVERSION1FINALFINALoutp
new: 29/02/2020 :programming :truebasic, divide window ,version 1.0
download (TrueBasic,code):TRUEPROGDIVIDEVERSION1FINAL
download (TrueBasic,outp):TRUEPROGDIVIDEVERSION1FINALoutp
Programming :'Maxima'
=====================
===============================================================================
tutorial:http://maxima.sourceforge.net/docs/tutorial/en/gaertner-tutorial-revision/Contents.htm
answer :https://stackoverflow.com/search?q=Maxima
===============================================================================
new: 10/04/2018 :programming 'block statement' 'version 1.0'
rem: use 'return([...,...,...])',use 'loop ,...,... go(loop)' : basic : goto
download (maxima,code):blockstatementexplainfinalversion1
download (Maxima,png) :blockstatementexplainfinalversion1maximaoutp
new: 12/07/2018 :programming 'use rules' 'version 1.0'
rem: use 'tellsimp,tellsimpafter,let,letsimp,.....'
rem: use 'remrule,remlet,freeof,mathchdeclare,option....'
download (maxima,code):howuserulesmaximacommandversion1final
download (Maxima,png) :howuserulesmaximacommandversion1finaloutp
new: 30/10/2018:sumtest , version 1.0
download (Maxima,code) :sumtestversion1finalversionfinal
download (Maxima,png) :sumtestversion1finalversionfinalimage
new: 15/11/2018:sum and powerseries , version 1.0
download (Maxima,code) :sumandpowerseriessomeaspectsversion1final
download (Maxima,png) :sumandpowerseriessomeaspectsversion1finalpng
new: 19/11/2018:tutorial : sum and products ,version 1.0
download (Maxima,code) :tutorialsimplesumproductsversion1final
download (Maxima,png) :tutorialsimplesumproductsversion1finaloutp.png
new: 20/11/2018:appendix : change propêrty of sum 'linear',matchdeclare , 'version 1.0'
download (Maxima,code) :appendixpropertiessumdeclarefeaturefunction
download (Maxima,png) :appendixpropertiessumdeclarefeaturefunctionoutp
new: 20/11/2018:maxima :find local max,min,version 1.0, see : 'above', Excel
new: 19/04/2019:programming :control when evaluation sum , version 1.0.
download (Maxima,code) :programmingcontrolevsumvers1
download (Maxima,png) :programmingcontrolevsumvers1outp
new: 29/05/2019:programming :Maxima :bubble sort with two for next loops, version 1.0.
download (Maxima,code) :Maximabubblesortwithtwoforloopsversion1final
download (Maxima,png) :Maximabubblesortwithtwoforloopsversion1finaloutp
new: 31/05/2019:programming :Maxima :while with 'example bubblesort',version 1.0
download (Maxima,code) :programmaximawhilebubblesortversion1final
download (Maxima,png) :programmaximawhilebubblesortversion1finaloutp
new: 31/05/2019:programming : Lagrange interpolation polynomial (version 1.0)
download (Maxima,code) :programlagrangeinterpolversion1final
download (Maxima,png) :programlagrangeinterpolversion1finaloutp
new: 31/05/2019:programming : least square method ,version 1.0
download (Maxima,code) :programleastsquaremethodversion1final
download (Maxima,png) :programleastsquaremethodversion1finaloutp
new: 13/06/2019:programming : simple example : book found corrected for the new version Maxima.
ref : maxima.sourceforge.net/docs/maximabook/maximabook-19-Sept-2004.pdf
download (Maxima,code) :programexamplebooknewdiffversion1final
download (Maxima,png) :programexamplebooknewdiffversion1finaloutp
new: 19/06/2019:programming : programming examples: maxima book ( 'use maxima commands')
ref :http://michel.gosse.free.fr/documentation/fichiers/maximabook.pdf
download (Maxima,code) :maximaexamplesmaximacommand
download (Maxima,png) :maximaexamplesmaximacommandoutp
new: 19/06/2019:programming : how to enter : data ,info ,etc
download (Maxima,code) :maximaprogrammingenterversion1final
download (Maxima,png) :maximaprogrammingenterversion1finaloutp
new:09/08/2019:programming:appendix ('nth order derivative,laplace transform'),version 1.0
download (Maxima,code) :icomplexappendixlaplacetrnorderderversion1final
download (Maxima,png) complexappendixlaplacetrnorderderversion1finaloutp
new:27/08/2019: programming: general :Levi-Civita symbol (sub,position,value),version 1.0
download (Maxima,code) :maximaalgopermversion1finaltfinal
download (Maxima,png) :maximaalgopermversion1finaltfinaloutp
new: 29/08/2019: programming: general :Levi-Civita symbol(position,input),version 1.0 (while,for)
reason : for and while : for => exit , while => condition ( 'programming '),problem : Maxima
download (Truebasic,code) :FLUIDGENERALLEVICIVITASYMBOLPOSITIONVERSION1FINALCORwhile
download (Truebasic,code) :FLUIDGENERALLEVICIVITASYMBOLPOSITIONVERSION1FINALCORFOR
download (Truebasic,png) :fluidgeneralleviCivitasymbolpositioninputversion1afinaloutp
new: 29/08/2019: programming: general :Levi-Civita symbol(position,input,sub),version 1.0b
download (Truebasic,code) :FLUIDGENERALLEVICIVITASYMBOLPOSITIONINPUTSUBVERSION1bFINALfinal
download (Truebasic,png) :FLUIDGENERALLEVICIVITASYMBOLPOSITIONINPUTSUBVERSION1bFINALfinaloutp
new: 29/08/2019: programming: general :Levi-Civita symbol(position,input,sub),version 1.0c
download (Truebasic,code) :FLUIDGENERALLEVICIVITASYMBOLPOSITIONINPUTSUBVERSION1CFINALFINAL
download (Truebasic,png) :FLUIDGENERALLEVICIVITASYMBOLPOSITIONINPUTSUBVERSION1CFINALFINALoutp
new:17/09/2019: programming:'firstn,rest,first' , v(i:j), ' i,j = integer j > i :j-i+1',version 1.0'
download (Maxima,code) :maximaprogrammingextractvecpartsversion1final
download (Maxima,png) :maximaprogrammingextractvecpartsversion1finaloutp
new:21/10/2019: programming: programming list operations ,version 1.0
download (Maxima,code) :maximalistconstructlistwith choosevarversion1
download (Maxima,png) :maximalistconstructlistwith choosevarversion1outp
new: 07/01/2020:programming: def linspace : values between tb[1] & tb[2], nv = number of points.
see:57e) Binary distillation "database (use linspace) to draw Txy diagram(pressure = cte)".
download (Maxima,code) :appendixcontrollinpacemaximaversion1
download (Maxima,png) :appendixcontrollinpacemaximaversion1outp
new:18/01/2020:programming: rerange polynoom ,version 1.0
download (Maxima,code) :maximarerangeversion1final
download (Maxima,png) :maximarerangeversion1finaloutp
new:20/01/2020:programming: rerange codes ,txt =simplode(expr),version 1.0
download (Maxima,code) :maximaprogrerangetxtcombversion1final
download (Maxima,png) :maximaprogrerangetxtcombversion1finaloutp
new:22/01/2020:programming: random walk ([N,S,W,E]),version 1.0
rem : see True Basic Programming
download (Maxima,code) :maximarandomwalknversion1final
download (Maxima,png) :maximarandomwalknversion1finaloutp
download (info example,pdf):TRUERADOMWALKVERSION1pdf
new:14/02/2020:programming: recursion Ackermann function 1.0
rem : see True Basic Programming
download (Maxima,code) :programrecursionackermannversion1finalfinal
download (Maxima,png) :programrecursionackermannversion1finalfinaloutp
new:26/04/2020:programming: back substitution for list of elements,version 1.0
download (Maxima,code) :maximaprogiterationbacksubstfinalversion1
download (Maxima,png) :maximaprogiterationbacksubstfinalversion1outp
new:27/04/2020:programming: 'defrule' ,version 1.0b
ref : rules and patterns in Maxima
download (Maxima,code) :maximaprogdefruleversion1final
download (Maxima,png) :maximaprogdefruleversion1finaloutp
download (Maxima,code) :maximaprogdefruleversion1final1a
download (Maxima,png) :maximaprogdefruleversion1final1aoutp
download (Maxima,code) :maximaprogdefruleversion1final1b
download (Maxima,png) :maximaprogdefruleversion1final1boutp
new:16/05/2020:programming: 'automatic generation of finite difference',version 1.0
download (Maxima,code) :maximaprogautomaticgeneqnsversion1final
download (Maxima,png) :maximaprogautomaticgeneqnsversion1finaloutp
new:17/05/2020:programming: different plots on the same canvas ,version 1.0
download (Maxima,code) :maximaprogrammingmultipleplotsononecanvasversion1final
download (Maxima,png) :maximaprogrammingmultipleplotsononecanvasversion1finaloutp
new:07/06/2020:programming: general function ,version 1.0
download (Maxima,code) :maximaprogramminggeneralfunctionversion1
download (Maxima,png) :maximaprogramminggeneralfunctionversion1outp
new:06/12/2020:programming: maxima: backsubst ( = list structure),version 1.0
download (Maxima,code) :maximabacksubstofliststructureversion1final
download (Maxima,png) :maximabacksubstofliststructureversion1finaloutp
defrule:
new: 13/09/2020:maxima :appendix (defrule),"del & diff ,myintegration version 1.0a, corrected
download (Maxima,code) :defruleimyntegrateversion1finalcorrected13092020
download (Maxima,png ) :defruleimyntegrateversion1finalcorrected13092020outp
lambda:(degree : function)
new: 31/01/2021:maxima :appendix : study of polynomial properties,version 1.0
download (Maxima,code) :appendixpolynomialpropertiesversion1final
download (Maxima,png ) :appendixpolynomialpropertiesversion1finaloutput
Graphics :
TrueBasic,Maxima:
=================
part 1 :general
=============
new: 17/01/2017 : How to make lin-log10 paper.(intro)
download (maxima,code):linlog10introfinalmaxima
download (maxima,html):linlog10introfinalmaximahtml
new: 20/01/2017 : How to make lin-log10 paper.(intro)
download (TrueBasic,code) : linlog10introtruebasicfinalversion1
download (TrueBasic,outp) :linlog10introtruebasicfinalversion1output
new: 24/01/2017 :paper lin-log10 .(final),normal version
how to use : box lines 'to draw a box'
download (TrueBasic,code) :paperlinlogxyfinal
download (TrueBasic,outp) :paperlinlogxyfinaloutput
new: 25/01/2017 :paper lin-log10 .(final),sub version
how to use : box lines 'to draw a box'
download (TrueBasic,code) :paperlinlogxyfinalsubfinal
download (TrueBasic,outp) :paperlinlogxyfinalsubfinaloutput
new: 25/01/2017 :paper log10-log10 .(final),normal version (version 1.0)
how to use : box lines 'to draw a box'
download (TrueBasic,code) :paperloglogxyfinalfinal
download (TrueBasic,outp) :paperloglogxyfinalfinaloutput
new: 25/01/2017 :paper log10-log10 .(final),sub version (version 1.0)
how to use : box lines 'to draw a box'
download (TrueBasic,code) :paperloglogxyfinalfinalsubfinal
download (TrueBasic,outp) :paperloglogxyfinalfinalsubfinaloutput
new: 27/06/2017 :'zero energy' (version 1.0)
http://www.antinews.in/secret-behind-numbers-3-6-9-finally-revealed/
how to : draw figure on the canvas (2d)
download (TrueBasic,code) :zeroenergyversion1
download (TrueBasic,outp) :zeroenergyversion1png
new: 27/06/2017 :'torus (vortex)' (version 1.0)
how to : draw figure on the canvas (2d)
how to draw - a Torus (Vortex) - step by step tutorial (english)
https://www.youtube.com/watch?v=P2z1EAihGNY
download (TrueBasic,code) :vortexmathversion1
download (TrueBasic,outp) :vortexmathversion1png
new: 27/06/2017 :'torus (3D )' (version 1.0)
how to : draw figure on the canvas (3d->2d)
3d: real world (parametric equation of torus (=donut))
x = (b+a*cos(theta))*cos(phi)
y = (b+a*cos(theta))*sin(phi)
z = a*sin(theta)
2d: projection
method 1 : 45 degree oblique projection
xs = y - x/2
ys = z - x/2
method 2 : method 1 ( x=0)
download (TrueBasic,code) :drawtorus3dwireframeversion1final
download (TrueBasic,outp) :drawtorus3dwireframeversion1finalpng
new: 11/07/2017 :Math (circle-line) 'version 1.0'
(use:'zero energy' (version 1.0) )
see :teacher: (tools) =>LaTeX output (*.tex)
circle : (x-a)^2+(y-b)^2 = r^2 => a,b,r
( center = (a,b),radius = r )
line : y = m*x+n ( a*x+b*y+c = 0 ) => m,n
( m = -a/b , n = -c/b )
1e) line-line
2e) line-Circle
3e) Circle-Circle ( example),appendix
download (maxima,code ):mathcirclelinefinalversion1afinal
download (maxima,code,png ):mathcirclelinefinalversion1apng
download (maxima,tex,before):mathcirclelinefinalversion1afinabefore
download (maxima,tex,after ):mathcirclelinefinalversion1atest2
download (maxima,pdf ,after):mathcirclelinefinalversion1afinal
appendix: (always open code ,maxima)
download (maxima,code ):circlemaximaappendix1
download (maxima,code ,png ):circlemaximaappendix1png
new: 10/04/2018 :Draw triangle mesh 'version 1.0'
see : menu above : extra 'draw a trianglemesh (version 1.0)',split screen in two parts.
download (TrueBasic,outp) : drawtrianglemeshversion1
new: 22/12/2018:graphics : How to draw lines with parametricplot,vertical,horizontal lines,version 1.0
download (Maxima,code) :howtodrawlineswithparametricplotversion1final
download (Maxima,png) :howtodrawlineswithparametricplotversion1finaloutp
new: 10/08/2019:graphics : (graphics:draw),more than one parametric plot on the canvas, version 1.0
download (Maxima,code) :programmingmaximamorethanoneparplotcanvasversion1final
download (Maxima,png) :programmingmaximamorethanoneparplotcanvasversion1finaloutp
new: 11/08/2019: graphics :programming : 'phase plane' from RK(=rk) output ,version 1.0
How to use : double y axis
How to get : rk; data,plot
How to get :wxphaseplot2d(s):=wxplot2d([discrete,makelist([p[2],p[3]],p,s)],[xlabel,""],[ylabel,""]);
download (Maxima,code) :phaseplanerefversion1finalfinal
download (Maxima,png) :phaseplanerefversion1finalfinaloutp
new: 16/05/2020: graphics :programming : different plots on the same canvas ,version 1.0
download (Maxima,code) :maximagraphicsmultipleplotsononecanvasversion1final
download (Maxima,png) :maximagraphicsmultipleplotsononecanvasversion1finaloutp
new: 26/11/2020: graphics :programming : geometry , version 1.0a,update the code
Euler line :https://andrejv.wordpress.com/2010/01/11/the-euler-line-of-a-triangle/
download (Maxima,code) :maximaintrogeometryprogversion1upgraphfinal
download (Maxima,png) :maximaintrogeometryprogversion1upgraphfinaloutp
download (Maxima,code) :maximaintrogeometryprogversion1aupgraphfinal
download (Maxima,png) :maximaintrogeometryprogversion1aupgraphfinaloutp
new: 02/12/2020: graphics :programming : maxima,packages draw 3d, intro : version 1.0
download (Maxima,code) :maximadrawinto3dintroversion1final
download (Maxima,png) :maximadrawinto3dintroversion1finaloutp
part 2 :graph (relation between : user coordinates - pixels)
====================================================
new: 09/02/2019:How to make picture from the canvas (*.BMP),version 1.0
download (Truebasic,code) :CANVASWRITEIMAGEUSERCOORDVERSION1FINAL
download (Truebasic,png) :CANVASWRITEIMAGEUSERCOORDVERSION1FINALoutp
new: 09/02/2019:Graph pixel : part 1 , version 1.0
download (Truebasic,code) :graphpixelpart1
download (Truebasic,png) :graphpixelpart1outp
new: 09/02/2019:Computation : pixels coordinates to user coordinates ,version 1.0
download (Maxima,code) :maximapixeltousergraphcoordinatesversion1final
download (Maxima,png) :maximapixeltousergraphcoordinatesversion1finaloutp
new: 10/02/2019:Graph pixel : part 2, version 1.0
download (Truebasic,code) :graphpixelpart2final
download (Truebasic,png) :graphpixelpart2finaloutp
new: 10/02/2019:Graph pixel : part 2a, version 1.0 ,save picture: *.bmp
download (Truebasic,code) :graphpixelpart2afinal
new: 10/02/2019:Graph pixel : part 2b, sub version 1.0 ,save picture: *.bmp
download (Truebasic,code) :graphpixelpart2bfinalsub
new: 18/02/2019:Graph pixel : part 2c, sub,draw circle version 1.0 ,save picture: *.bmp
download (Truebasic,code) :GRAPHPIXELPART2CFINALSUB
download (Truebasic,jpeg) : funcpict2cjpeg.jpg
new: 19/02/2019:Graph user coordinates : part 3, sub,draw circle,aspectratio version 1.0 ,save picture: *.bmp
download (Truebasic,code) :graphuserpart3finalsub
download (Truebasic,jpeg) :funcpict3jpeg
new: 19/02/2019:Graph user-pixel coord.:part4 save output of a program (*.bmp) version 1.0
download (Truebasic,code) :graphuserpixelpart4finalsub
math (2022)
________________
calculus: (important topics)
https://en.wikipedia.org/wiki/Leibniz_integral_rule
1e)Derrvative under the integral sign
new: 15/08/2019:Calculus : Leibniz's rule for differentiation under the integral sign (one variable),version 1.0a
example 1: youtube
download (Maxima,code) :calculusleibnitzrule1diffintegralsignwithonevarversion1afinal
download (Maxima,png) :calculusleibnitzrule1diffintegralsignwithonevarversion1afinaloutp
new: 16/08/2019:Calculus : Leibniz's rule for differentiation under the integral sign (two variables),version 1.0
example 2:youtube
download (Maxima,code) :calculusleibnitzrule1diffintegralsignwithtwovarversion1final
download (Maxima,png) :calculusleibnitzrule1diffintegralsignwithtwovarversion1finaloutp
new: 16/08/2019:Calculus :proof: Leibniz's rule for differentiation under the integral sign (two variables),version 1.0
download (Maxima,code) :calculusleibnitzrule1diffintegralsignwithtwovarproofversion1final
download (Maxima,png) :calculusleibnitzrule1diffintegralsignwithtwovarproofversion1finaloutp
2e)First & Second Fundamental Theorem of Calculus.
example 3: youtube
example 4: youtube
new: 12/08/2019:Calculus : First Fundamental Theorem of Calculus(proof),part 1,version 1.0
download (Maxima,code) :Fundamentaltheoremcalculuspart1version1final
download (Maxima,png) :Fundamentaltheoremcalculuspart1version1finaloutp
new: 12/08/2019:Calculus : Second Fundamental Theorem of Calculus(proof),part 2 ,version 1.0
download (Maxima,code) :Fundamentaltheoremcalculuspart2version1final
download (Maxima,png) :Fundamentaltheoremcalculuspart2version1finaloutp
3e)Integration by parts Calculus.
new: 12/08/2019:Calculus : integration by parts ,version 1.0 (functions: PI)
download (Maxima,code) :calculusintegrationbypartsversion1final
download (Maxima,png) :calculusintegrationbypartsversion1finaloutp
4e)double integral to a single integral.
rem : BVP ( = Boundary Value Problem) to a IE (= Integral Equation)
new: 21/08/2019:Calculus : double integral to a single integral ,version 1.0
download (Maxima,code) :calculusdoubleintegraltosingleintegralintegraleqversion1final
download (Maxima,png) :calculusdoubleintegraltosingleintegralintegraleqversion1finaloutp
5e)triple integral to a single integral.
new: 22/08/2019:Calculus : triple integral to a single integral ,version 1.0
download (Maxima,code) :calculusdoubleintegraltosingleintegralintegraleqversion1finalextra
download (Maxima,png) :calculusdoubleintegraltosingleintegralintegraleqversion1finalextraoutp
application : 3e),4e),5e), "Volterra Integral Equations & ode",use : load(inteqn);
===================
new: 10/06/2020:Calculus : Volterra Integral Eqn and ODE,version 1.0
download (Maxima,code) :calculusvolterraintegreqandodeversion1
download (Maxima,png) :calculusvolterraintegreqandodeversion1outp
Dirac Delta Function
=================
6e)representation
new: 10/02/2020:Calculus : representation : dirac-delta function ,version 1.0
download (Maxima,code) :maximadiracdelrepresversion1final
download (Maxima,png) :maximadiracdelrepresversion1finaloutp
7e)delta(g(x))
new:11/02/2020:Calculus : Dirac Delta of function , version 1.0
download (Maxima,code) :maximainverseidentitiesof thesumversion1
download (Maxima,png) :maximainverseidentitiesof thesumversion1outp
8e)delta(c*x) = delta(x)/abs(c), c=constant,scaling property
new: 11/02/2020:Calculus : scaling property delta(c*x) ,version 1.0
download (Maxima,code) :appendixscalingpropdiracdeltaversion1final
download (Maxima,png) :appendixscalingpropdiracdeltaversion1finaloutp
9e)differentation of dirac delta function
new: 18/02/2020:Calculus : derivatives of the delta function , version 1.0a
download (Maxima,code) :maximaderivativesdeltafunctionversion1final
download (Maxima,png) :maximaderivativesdeltafunctionversion1finaloutp
download (Maxima,code) :maximaderivativesdeltafunctionversion1afinal
download (Maxima,png) :maximaderivativesdeltafunctionversion1afinaloutp
10e) appendix :integration conversion,vesion 1.0
new: 18/02/2020:Calculus : maxima :appendix integration conversion,vesion 1.0
download (Maxima,code) :programmaximaintegrationconverseversion1final
download (Maxima,png) :maximaderivativesdeltafunctionversion1afinaloutp
11e) under integral sign nth power derivative dirac delta from g(x).
new: 07/03/2020:Calculus : nth power derivative for dirac-delta function from g(x) under integral sign ,version 1.0
download (Maxima,code) :nthpowerdiracwithargumentgunderintegralsignversion1final
download (Maxima,png) :nthpowerdiracwithargumentgunderintegralsignversion1finaloutp
download (doc,pdf) :diracdir1
download (Maple,code ) :peterdeltadiffupn ( Prof Dr.Denis Constales ,UGent)
new: 12/03/2020:theoretical aspect
download (Maxima,code1) :theorynthderivativediracdeltagxunderintegralsignversion1final
download (Maxima,png1 ) :theorynthderivativediracdeltagxunderintegralsignversion1finaloutp
f(x),z=f(x,y) : tangent line,normal line,tangent plane.
==========================================
12e) how construct f(x),tangent line @ normal line (2d)
new: 20/03/2020:Calculus : How to construct : z=f(x,y), tangent plane,tangent line,version 1.0,part1.
download (Maxima,code) :maximaffxytangentplandlineversion1finalpart1
download (Maxima,png) :maximaffxytangentplandlineversion1finalpart1outp
13e) how construct z=f(x,y),tangent plane @ normal line(3d)
new:21/03/2020:Calculus : How to construct : z=f(x,y), tangent plane,tangent line,version 1.0,part2.
ref : 3d graphics maxima
download (Maxima,code) :maximaffxytangentplandlineversion1finalpart2
download (Maxima,png) :maximaffxytangentplandlineversion1finalpart2outp
14e) how construct z=f(x,y),tangent plane @ normal line(3d,concept =gradient)
new: 27/03/2020:Calculus : How to construct : z=f(x,y), tangent plane,tangent line,version 1.0a,part3.
download (Maxima,code) :maximaffxytangentplandlineversion1finalpart3a
download (Maxima,png) :maximaffxytangentplandlineversion1finalpart3aoutp
Hamiltonian Function
==================
15e) hamiltonian
new: 29/03/2020:Calculus : maxima hamiltonian function ,version 1.0,part 1
download (Maxima,code) :maximahamiltonianfunctioversion1part1
download (Maxima,png) :maximahamiltonianfunctioversion1part1outp
16e) hamiltonian (= example)
new:29/03/2020:Calculus : maxima hamiltonian function ,version 1.0,part 2
download (Maxima,code) :maximahamiltonianfunctioversion1part2
download (Maxima,png) :maximahamiltonianfunctioversion1part2outp
17e) hamiltonian (= example:physics ,F=-k*x , H(x,y) -> H(p,q) =T+V=T(p)+V(q)
new:29/03/2020:Calculus : maxima hamiltonian function ,version 1.0,part 3
download (Maxima,code) :maximaffxytangentplandlineversion1finalpart3
download (Maxima,png) :maximaffxytangentplandlineversion1finalpart3outp
18e) hamiltonian (= example:physics ,Schrödinger ( H*ψ(x) = E*ψ(x)),H = p^2/(2*m)+v)
new:30/03/2020:Calculus : maxima hamiltonian function ,version 1.0,part 4
download (Maxima,code) :maximaffxytangentplandlineversion1finalpart4
download (Maxima,png) :maximaffxytangentplandlineversion1finalpart4outp
Legendre Transformation
======================
19e) Legendre transformation (thermodynamics: H:enthalpy,G:Gibbs Free Energy,F:Helmholtz ....
new: 31/03/2020:Calculus : maxima : intro legendre transformation( = thermodynamics),H,G,F , version 1.0
download (Maxima,code) :maximalegenfdretrthermohgfversion1final
download (Maxima,png) :maximalegenfdretrthermohgfversion1finaloutp
20e) Legendre transformation :theoretical approach
new: 01/04/2020:Calculus : maxima :theoretical legendre transformation,version 1.0a
download (Maxima,code) :maximatheoreticallegendretransfversion1final
download (Maxima,png) :maximatheoreticallegendretransfversion1finaloutp
download (Maxima,code) :maximatheoreticallegendretransfversion1afinal
download (Maxima,png) :maximatheoreticallegendretransfversion1afinaloutp
ODE ( & infinite sum & multiple RK4)
==================
21e) math:solve ode with infinite sums( intro)
new: 21/04/2020:Calculus : math:solve differential equations with infinite sums( intro),version 1.0
download (Maxima,code) :mathsolvediffeqwithinfsumversion1finalintro
download (Maxima,png) :mathsolvediffeqwithinfsumversion1finalintrooutp
22e) math:solve ode with infinite sums(example).
new: 21/04/2020:Calculus : math:solve differential equations with infinite sums(example),version 1.0
download (Maxima,code) :mathsolvediffeqwithinfsumversion1finalexample
download (Maxima,png) :mathsolvediffeqwithinfsumversion1finalexampleoutp
23e) math:solve ode with multiple RK4
new: 06/06/2020:Calculus : multiple odes rk4 ,version 1.0a (x0,x1,x2,.....)
download (Maxima,code) :maximamultiplerk4finalversion1a
download (Maxima,png) :maximamultiplerk4finalversion1aoutp
new: 17/06/2020:Calculus : multiple odes rk4 ,version 1.0b (x[0],x[1],x[2],.....)
download (Maxima,code) :maximamultiplerk4tfinalfinalversion1b
download (Maxima,png) :maximamultiplerk4tfinalfinalversion1boutp
24e) math:power series,'intro'
youtube :https://www.youtube.com/watch?v=V1AKAkGJlN8
new: 13/11/2020:Calculus : maxima :intro powerseries, version 1.0
download (Maxima,code) :maximaintropowerseriesversion1final
download (Maxima,png) :maximaintropowerseriesversion1finaloutp
25e) math:Maclauren,Taylor series,'intro'
new: 14/11/2020:Calculus : maxima :intro powerseries, maclauren,taylor series,version1.0
download (Maxima,code) :maximamactaylorseriesversion1final
download (Maxima,png) :maximamactaylorseriesversion1finaloutp
integration : with load(antid),2021
=============================
26e)new: 05/08/2021:Calculus : Maxima : math :use antidiff = integration , version 1.0
download (Maxima,code) :maximamathuseantidiffversion12021.wxmx
download (Maxima,png) :maximamathuseantidiffversion12021outp
Geometry
=========
27e) new: 12/09/2021:maxima : math :surface area of a plane,version 1.0
download (Maxima,code) :maximamathareaofplaneversion12021
download (Maxima,png) :maximamathareaofplaneversion12021outp
?e) how construct z=f(x,y),tangent plane @ normal line
new: ?/03/2020:Calculus : How to construct : z=f(x,y), tangent plane,tangent line,version 1.0,part2.
download (Maxima,code) :maximaffxytangentplandlineversion1finalpart2
download (Maxima,png) :maximaffxytangentplandlineversion1finalpart2
matrix: (important topics
= > Matrix cookbook
=> Matrix & Vector
1e) (A^(-1) + B^(-1)) ^(-1) = A.(A+B)^(-1).B = B.(A+B)^(-1).A
= > Matrix Inversion Identities
new: 14/10/2019:Algebra ,inverse sum of two matrix(both inverse),version 1.0
download (Maxima,code) :maximainverseidentitiesof thesumversion1
download (Maxima,png) :maximainverseidentitiesof_thesumversion1outp
2e) a: row reduced echelon form (rows = columns,matrix), online code found
new: 16/10/2019:Reduced row echelon from matrix , version 1.0
download (Maxima,code) :Maximarowreducedechelonformversion1
download (Maxima,png) :maximarowreducedechelonformversion1outp
b: row reduced echelon form (rows<> columns,matrix)
How to use :
new: 19/10/2019 : maxima :dependencies between reaction and components (<=>),version(1.0)
download (Maxima,code) :maximadependenciesbetweenreactionandcompbothwiseversion1
download (Maxima,png) :maximadependenciesbetweenreactionandcompbothwiseversion1outp
new: 19/10/2019:general code "reduced row echelon form of a matrix : (rows ≠ columns )",version 1.0
=> ref : Prof Denis Constales UGent ( maple code)
download (Maxima,code) :maximadenisreducedrowechelonmatrixversion1
download (Maxima,png) :maximadenisreducedrowechelonmatrixversion1outp
download (Maple,code ) :peterrref
download (Maxima,png) :peterrrefoutp
download (TrueBasic,code) :TRUEBASICRREFDATAVERSION1final
download (Truebasic,png) :TRUEBASICRREFDATAVERSION1finaloutp
3e) matrix simplification rules without implementation the rules your self
new: 20/10/2019:Algebra ,maxima : matrix simplification rules without implementation the rules your self,version 1.0
download (Maxima,code) :maximalinearmatrixrulesprogrammingversion1
download (Maxima,png) :maximalinearmatrixrulesprogrammingversion1outp
4e) power of a matrix .
new:03/02/2020:matrix : power of a matrix ( = Fibonacci sequence).,part 1
download (Maxima,code) :maximamatrixpowfibonacciseqversion1finalpart1
download (Maxima,png) :maximamatrixpowfibonacciseqversion1finalpart1outp
new:03/02/2020:matrix : power of a matrix ( = Fibonacci sequence).,part 2
download (Maxima,code) :maximamatrixpowfibonacciseqversion1finalpart2
download (Maxima,png) :maximamatrixpowfibonacciseqversion1finalpart2outp
appendix: A ( =matrix )
load("diag")
f(x) := x^k;
mat_function (f, A);
new:03/02/2020:: matrix to a power : A^^k (Numerical, Symbolic,'diag') ,version 1.0
download (Maxima,code) :maximaappendixpowmatversion1final
download (Maxima,png) :maximaappendixpowmatversion1finaloutp
5e)Matrix Diagonalization
see : youtube ,https://www.youtube.com/watch?v=VYS9EYZ3gC
new:19/02/2020:: matrix :appendix : diagonalization,complex matrix.
download (Maxima,code) :maximadiagonalizationmatrixcomplexversion1final
download (Maxima,png) :maximadiagonalizationmatrixcomplexversion1finaloutp
System Differential Equations (ref : MIT) :
Cooling Law 'Newton' = system of differential equations : X'=A*X
ref:MIT OpenCourseWare:https://ocw.mit.edu/courses/audio-video-courses/
mathematics ' differential equations'
Lecture 24: Introduction to First-order Systems of ODEs
Lecture 25: Homogeneous Linear Systems with Constant Coefficients
Lecture 26: Continuation: Repeated Real Eigenvalues
new: 24/03/2017:part1,module1 : 'eigenvalues' and 'eigenvectors'
download (Maxima,code) :module1diffeqswitheigenvalueeigenvectorfinalversion1
download (Maxima,html) :module1diffeqswitheigenvalueeigenvectorfinalversion1html
new: 25/03/2017:part2,module2 : 'solve system : differential equations 2 by 2 '
download (Maxima,code) :module2diffeqsystem2by2finalversion1
download (Maxima,html) :module2diffeqsystem2by2finalversion1html
new: 10/10/2017:part2a,module2 : 'solve system : differential equations 2 by 2 ',laplace transform
download (Maxima,code) :module2alaplacetransformode2by2version1
download (Maxima,png) :module2alaplacetransformode2by2version1outp
new: 25/03/2017:part3,module3 : 'cooling law ,three zone problem'
download (Maxima,code) :module3coolinglawfinalversion1
download (Maxima,html) :module3coolinglawfinalversion1html
new: 26/03/2017:appendix : 'general system differential equations 2 by 2'
download (Maxima,code) :appendixcoolinglawgeneralfinalversion1
download (Maxima,html) :appendixcoolinglawgeneralfinalversion1html
new: 26/03/2017:appendix : 'repeated eigenvalues ,system diff.eq 3 by 3,solve'
download (Maxima,code) :appendixrepeatedveigenvaluesfinalversion1
download (Maxima,html) :appendixrepeatedveigenvaluesfinalversion1html
new: 26/03/2017:appendix : 'complex eigenvalues ,system diff.eq 2 by 2,solve'
simple:
download (Maxima,code) :appendixcomplexeigenvaluesfinalversion1
download (Maxima,html) :appendixcomplexeigenvaluesfinalversion1html
plot: revision1
download (Maxima,code) :appendixcomplexeigenvaluesfinalversion1revision1
download (Maxima,html) :appendixcomplexeigenvaluesfinalversion1revision1html
plot: show that plot = 'ellipse' (28/03)
download (Maxima,code) :appendixellipsphaseplotcomplexrealpartfinalversion1
download (Maxima,html) :appendixellipsphaseplotcomplexrealpartfinalversion1html
ODE : Laplace Transformation
(O) rdinary (D)ifferential (E)quations
ref:MIT OpenCourseWare:https://ocw.mit.edu/courses/audio-video-courses/
new: 19/09/2017: appendix : calculation residue a(-1)
download (Maxima,code) :appendixresiduedefinitionfinalversion1
download (Maxima,png) :appendixresiduedefinitionfinalversion1outtp
new: 19/09/2017: :intro1 : Laplace Transformation ( residue = f(s)*e^(st),inverse).
download (Maxima,code) :residuecalcintrolaplace1
download (Maxima,png) :residuecalcintrolaplace1outp
new: 20/09/2017: :intro2 : Inverse Laplace Transformation with infinitely many singularities.
cosh(z) = cos(i*z)
i*sinh(z) = sin(i*z)
rem : i=sqr(-1)=sqrt(-1); z=a+i*b;a,b real numbers
download (Maxima,code) :infinitelymanysingularatiesversion
download (Maxima,png) :infinitelymanysingularatiesversion1outp
new: 21/09/2017: :intro3 : Find zero values Cosh(z)=0 , z = x+i*y, relation to Cos(i*z) and log(z).
download (Maxima,code) :findzerocoshcomplexplaneversion1
download (Maxima,png) :findzerocoshcomplexplaneversion1outp
new: 28/09/2017: :intro4 : Find f = f(x), given :p=p(x),q=q(x), df/dx+p*f = q => Laplace Transformation.
special functions for mathematics: erf(z)+erfc(z) = 1,gamma_incomplete(a,z)
info: see *. png
download (Maxima,code) :laplacefirstoderodefinalversion1
download (Maxima,png) :laplacefirstoderodefinalversion1outp
new: 28/09/2017: :intro5 : Convolution theorema :f*g = integrate(f(u)*g(t-u),u,0,t) relation F(s).G(s).
code : F(s).G(s) = L^(-1) {F(s).G(s)}
L^{f(t)} = Laplace Transform of f(t) => f(s)
L^(-1){f(s)} = Inverse Laplace Transform of f(s) => f(t)
download (Maxima,code) :convolutiontheoremalaplaceversion1
download (Maxima,png) :convolutiontheoremalaplaceversion1outp
new: 28/09/2017: example : L^(-1){F(s).G(s)} with use Convolution theorema.
download (Maxima,code) :exampleconvolutioninverselaplacetransformversion1
download (Maxima,png) :exampleconvolutioninverselaplacetransformversion1outp
new: 28/09/2017: appendix : Bessel Differential Equations (t^2*y''+t*y'+(t^2-n^2)*y=0 ,n=value)
special functions for mathematics: bessel_y(n,t),bessel_j(n,t)
=> load('contrib_ode)$
download (Maxima,code) :Besselequationloadcontribodeloadversion1
download (Maxima,png) :Besselequationloadcontribodeloadversion1outp
new: 29/09/2017:find L{ Jo(t)} ? (t^2*y''+t*y'+(t^2-n^2)*y=0 ,n=0) ,theorema 1
Laplace transform of Bessel function of order zero
youtube :https://www.youtube.com/watch?v=II_JUVmSDa8
theorema 1 = Initial-value theorem.
limit(F(t)),t,0) = limit(s*f(s),s,infinity)
theorema 2 = Final-value theorem.
limit(F(t)),t,infinity) = limit(s*f(s),s,0)
download (Maxima,code) :Besselequationlaplacetransformfindjotversion1
download (Maxima,png) :Besselequationlaplacetransformfindjotversion1outp
new: 29/09/2017:find L{ Jo(t)} ? with series Jo(t) = 1 -t^2/2+t^4/(2^2*4^2)-t^6/(2^2*4^2*6^2)........
rem :code (Maxima): ratdenomdivide:true$,eq20:ratexpand(eq19);
download (Maxima,code) :othermethodlaplactransformationjotversion1
download (Maxima,png) :othermethodlaplactransformationjotversion1outp
new: 30/09/2017:find f(x)=(1+x)^m = 1+m*x+(m*(m-1))/2*x^2+................(for L{ Jo(t}),binomial series.
rem :code (Maxima): infinite sum : sumcontract,factcomb,intosum.
download (Maxima,code) :findcoefakbinomialseriesfromtheodeversion1
download (Maxima,png) :findcoefakbinomialseriesfromtheodeversion1outp
new: 30/09/2017:find appendix,binomial series (1+x)*df/dx = m*f,f(0)=1.
download (Maxima,code) :binomialseriesappendixversion1
download (Maxima,png) :binomialseriesappendixversion1outp
new: 04/10/2017:find ivp : t*y''+y'+4*t*y = 0,ic={ y(0) = 3,y'(0) =0).
download (Maxima,code) :Besseleqlaplacetransforminitialconditionstablesversion1
download (Maxima,png) :Besseleqlaplacetransforminitialconditionstablesversion1outp
new: 09/10/2017:find L{5*exp(-0.3*t)*unit_step(t-2)} ,delayed(=tau) exponential,unit_step(t-tau).
download (Maxima,code) :delayedsignalandlaplacetransformexponentialversion1
download (Maxima,png) :delayedsignalandlaplacetransformexponentialversion1outtp
new: 09/10/2017:find ivp: y''(t) +2*y'(t)+5*y(t) = H(t),y(0)=y'(0)=0,H(t)=unit_step(t)-unit_step(t-pi).
shifting : L^(-1){exp(-k*s)*F(s)) = f(t-k)*unit_step(t-k), L{f(t)} = F(s) ,example : k = pi
download (Maxima,code) :solveivpproblemunitstepconstructionlaplaceversion1
download (Maxima,png) :solveivpproblemunitstepconstructionlaplaceversion1outp
new: 10/10/2017:find ivp: y''(t) +2*y'(t)+5*y(t) = H(t),y(0)=y'(0)=0,H(t)=unit_step(t)-unit_step(t-pi).
shifting : L^(-1){exp(-k*s)*F(s)) = f(t-k)*unit_step(t-k), L{f(t)} = F(s) ,version 1.1 (more graphics)
download (Maxima,code) :solveivpproblemunitstepconstructionlaplace1705version11
download (Maxima,png) :solveivpproblemunitstepconstructionlaplace1705version11outp
new: 25/03/2017:part2,module2 : 'solve system : differential equations 2 by 2 '
download (Maxima,code) :module2diffeqsystem2by2finalversion1
download (Maxima,png) :module2diffeqsystem2by2finalversion1outp
new: 10/10/2017:part2a,module2 : 'solve system : differential equations 2 by 2 ',laplace transform
see :Cooling Law 'Newton' = system of differential equations : X'=A*X (above)
rem :code (Maxima): desolve ( inside use laplace transform)
download (Maxima,code) :module2alaplacetransformode2by2version1
download (Maxima,png) :module2alaplacetransformode2by2version1outp
new: 25/03/2017:part3,module3 : 'cooling law ,three zone problem'
download (Maxima,code) :module3coolinglawfinalversion1
download (Maxima,png) :module3coolinglawfinalversion1outp
new: 11/10/2017:part3a,module3 : 'cooling law ,three zone problem',laplace transform
see :Cooling Law 'Newton' = system of differential equations : X'=A*X (above)
download (Maxima,code) :module3alaplacetransformcoolinglawversion1
download (Maxima,png) :module3alaplacetransformcoolinglawversion1outp
new: 13/10/2017: appendix : make list in Maxima.
download (Maxima,code) :appendixmakelistmaximaversion1
download (Maxima,png) :appendixmakelistmaximaversion1outp
new: 27/05/2018: Normal Form 'sec. order diff. eq. ','version 1.0'
download (Maxima,code) :transformlinsecorderdiffeqwithexample
download (Maxima,png) :transformlinsecorderdiffeqwithexampleoutp
see : SPECIAL TOPICS : below
PDE : numerical
(P)artial (D)ifferential (E)quations
new: 18/10/2017: appendix : dependencies variables.
download (Maxima,code) :exampledependspdeversion1
download (Maxima,png) :exampledependspdeversion1outp
new: 23/10/2017: three indices (lower index i,j one upper index k).
a(1,3,k+1)*b[2]+b[1]*a(1,2,k)=a(2,2,k+1)*b[4]+a(1,4,k)*b[3]
download (Maxima,code) :threeindicesequatioinsfinalexampleversion1
download (Maxima,png) :threeindicesequatioinsfinalexampleversion1outp
new: 01/11/2017: robin (b)oundary (c)ondition (three point backward differences)
robin bc : " x - direction " = > du/dx+c1*u = c2 , u=u(x,y)
robin bc : " y - direction " = > du/dy+c3*u = c4 , u=u(x,y)
download (Maxima,code) :BCthirdkindrobinfinalversion1
download (Maxima,png) :BCthirdkindrobinfinalversion1outp
new: 02/11/2017: Laplace equation 2D (numerical scheme)
diff(u,x,2) + diff(u,y,2) =0 (symbolic)
(u(i+1,j)+u(i,j+1)-4*u(i,j)+u(i,j-1)+u(i-1,j))/h^2=0 (numerical)
download (Maxima,code) :laplacepde2dnumericalschemefinalversion1
download (Maxima,png) :laplacepde2dnumericalschemefinalversion1outp
new: 03/11/2017: Mixed partial derivatives ∂/∂x(∂u/∂y) (numerical scheme)
diff(u,x,1,y,1) = diff(u,y,1,x,1) (symbolic)
(u(i+h,j+h)-u(i+h,j-h)-u(i-h,j+h)+u(i-h,j-h))/(4*h^2) (numerical)
download (Maxima,code) :mixedpartialderivativemaxiversion1final
download (Maxima,code) :mixedpartialderivativemaxiversion2final
download (Maxima,png) :mixedpartialderivativemaxiversion1finaloutp
download (Maxima,png) :mixedpartialderivativemaxiversion2finaloutp
new: 08/11/2017: Laplace equation 2D (numerical scheme),sor factor
Dirichlet Boundry condition ( = fixed value on the boundary),corrected 'version 1.1'
print "---------------------------------------------------------------------------"
print " sor = 0 , jacobi; sor = 1 Gauss Seidel "
print " sor < 1 ;underrelaxation,sor > 1 ;overrelaxation "
print "----------------------------------------------------------------------------"
( see also :19e) 2D-Laplace equation (steady = dT/dt = 0) 'advanced')
download (TrueBasic,code) :laplacechem2dfinaldifferentmethodsfinalversion11
download (TrueBasic,outp) :laplacechem2dfinaldifferentmethodsfinalversion11outp
download (TrueBasic,outp) :laplacechem2dfinaldifferentmethodsfinalversion11outpdatainput
new: 14/11/2017: Laplace equation 2D ' skewed coordinates',α = 0
download (Maxima,code) :laplaceobliquebothdirectionvufinal
download (TrueBasic,outp) :laplaceobliquebothdirectionvufinaloutp
new: 29/11/2017: (f)inite (v)olume (m)ethod = FVM, (flow with'BC')
Jx = u*T-tau*dT/dx, ('flux' x direction)
Jy = v*T-tau*dT/dy, ('flux' y direction)
d/dx(jx)+d/dy(jy) = 0, (v=0,u(y)=given,tau=kapa/(rho*c_p)),fully developed flow.
advection : UDS = Upwind Difference Scheme
diffusion : CDS = Central Difference Scheme
ref :numerical methods for partial differential equations
Finite Differential and Finite Volume Methods
(Sandip Mazumder),Elsevier.
download (TrueBasic,code) :finiteflowmethodflowchannelfinalversion1
download (TrueBasic,outp) :finiteflowmethodflowchannelfinalversion1outp
new: 14/12/2017: Laplace equation 2D (irregular boundary ,regular boundary)
irregular boundary (= irregular node) : h1,h2,h3,h4
grid spacing 'x' = h
grid spacing 'y' = k
arm length = h1,h2,h3,h4 , (east,north,west,south)
regular boundary (=regular node) : h1=h2=h3=h4=1
see:new: 02/11/2017: Laplace equation 2D (numerical scheme)
download (Maxima,code) :laplaceirregularboundary2D4differentarmsverrsion1maxima
download (Maxima,png) :laplaceirregularboundary2D4differentarmsverrsion1maximaoutp
new: 18/12/2017: Laplace equation 3D (cylindrical coordinate system: rho,phi,z),analyse
diff(u,x,2)+diff(u,y,2)+diff(u,z,2) =diff(u,rho,2)+1/rho*diff(u,rho)+1/rho^2*diff(u,phi,2)+diff(u,z,2)=0
download (Maxima,code) :laplaceequationcylindricalcoordinatesfinalversion1maxima
download (Maxima,png) :laplaceequationcylindricalcoordinatesfinalversion1maximaoutp
new: 21/12/2017: Laplace equation 3D (spherical coordinate system: rho=r,theta=th,phi=ph),analyse
diff(u,x,2)+diff(u,y,2)+diff(u,z,2) =1/r^2*diff(r^2*diff(u,r))+1/(r^2*sin(th))*diff(sin(th)*diff(u,th))+1/(r^2sin(th)^2)*diff(u,ph,2)
download (Maxima,code) :laplaceequationsphericalcoordinatefinalversion1
download (Maxima,png) :laplaceequationsphericalcoordinatefinalversion1outp
new: 23/12/2017: appendix :rectangular domain fill (boundaries ,inside domain)
use : "else if" construct (programming structure,basic)
download (TrueBasic,code) :boundariesanddomainfillversion1final
download (TrueBasic,outp) :boundariesanddomainfillversion1finaloutp
new: 27/01/2020: maxima : differences equation ( = how to use ),version 1.0
use : use : Δ = E -1,Δ^k =(E -1)^k, k =integer =1,2,3,4,5,......
download (Maxima,code) :maximadefdifferencesversion1finalfinal
download (Maxima,png) :maximadefdifferencesversion1finalfinaloutp
new: 23/01/2021: maxima : intersection 2d grid & circle ,version 1.0
download (Maxima,code) :maximaintersection2dgridcircleversion1final2021
download (Maxima,png) :maximaintersection2dgridcircleversion1final2021outp
new: 24/01/2021: maxima : intersection 2d grid & circle ,version 1.0a
download (Maxima,code) :maximaintersection2dgridcircleversion1afinal2021
download (Maxima,png) :maximaintersection2dgridcircleversion1afinal2021outp
new: 26/01/2021: maxima : simple way to construct 3D matrix,version 1.0
download (Maxima,code) :maximasimplemultidimensionalmatrixversion12021
download (Maxima,png) :maximasimplemultidimensionalmatrixversion12021outp
PDE : symbolic
improved : maxima version for inverse laplacetransform
download (Maxima,source) :laplaceinv
rem :see above
new: 11/12/2018:solve pde (part 1), use laplace transform. 'version 1.0'
download (Maxima,code) :solvepdewithlaplacepart1version1final
download (Maxima,png) :solvepdewithlaplacepart1version1finaloutp
new: 11/12/2018:solve pde (part 2), use laplace transform. 'version 1.0'
download (Maxima,code) :solvepdewithlaplacepart2version1final
download (Maxima,png) :solvepdewithlaplacepart2version1finaloutp
new: 11/12/2018:solve pde (part 3), use laplace transform. 'version 1.0'
download (Maxima,code) :solvepdewithlaplacepart3version1final
download (Maxima,png) :solvepdewithlaplacepart3version1finaloutp
new: 11/12/2018:solve pde (part 4), use laplace transform. 'version 1.0'
download (Maxima,code) :solvepdewithlaplacepart4version1final
download (Maxima,png) :solvepdewithlaplacepart4version1finaloutp
new: 11/12/2018:solve pde (part 5), use laplace transform. 'version 1.0'
download (Maxima,code) :solvepdewithlaplacepart5version1final
download (Maxima,png) :solvepdewithlaplacepart5version1finaloutp
new: 11/12/2018:solve pde (part 6), use laplace transform. 'version 1.0'
download (Maxima,code) :solvepdewithlaplacepart6version1final
download (Maxima,png) :solvepdewithlaplacepart6version1finaloutp
new: 11/12/2018:solve pde (part 7), use laplace transform. 'version 1.0'
download (Maxima,code) :solvepdewithlaplacepart7version1final
download (Maxima,png) :solvepdewithlaplacepart7version1finaloutp
new: 11/12/2018:solve pde (part 8), use laplace transform. 'version 1.0'
download (Maxima,code) :solvepdewithlaplacepart8version1final
download (Maxima,png) :solvepdewithlaplacepart8version1finaloutp
new: 11/12/2018:solve pde (part 9), use laplace transform. 'version 1.0'
download (Maxima,code) :solvepdewithlaplacepart9version1final
download (Maxima,png) :solvepdewithlaplacepart9version1finaloutp
new: 11/12/2018:solve pde (part ?), use laplace transform. 'version 1.0'
download (Maxima,code) :taylorexpansion2dversion1afinalsub
download (Maxima,png) :taylorexpansion2dversion1afinalsuboutp
SPECIAL TOPICS :
1e) integral equation
---------------------------------
intro:
=====
new: 03/10/2019: numerical integral : Maxima :Gaussian Quadrature ,version 1.0
----------------------------------------------------------------------------------------------------------------------------
download (Maxima,code) :maximagausslegendre2and2pointruleversion1final
download (Maxima,png) :maximagausslegendre2and2pointruleversion1finaloutp
fredholm equation of the second kind :
==================================
new: 09/01/2018: integral equation : fredholm equation of the second kind 'numerical'
-------------------------------------------------------------------------------------------------------------------------------------
=> phi(x) +integration(ker(x,t)*phi(t),t,a,b) = f(x)
solution : phi(x) = f(x) -(b-a)/6*sum(c(j)*ker(x,t(j))*phi(t(j)),j,0,n)
----------------------------------------------------------------------------------------
example : t(0),t(1),t(2) => phi(0),phi(1),phi(2)
----------------------------------------------------------------------------------------
ker = kernel from the ' integral equation '
----------------------------------------------------------------------------------------
download (TrueBasic,code) :intergralequationfredholmfinalversion11
download (TrueBasic,outp1) :intergralequationfredholmfinalversion11outp
download (TrueBasic,code) :INTERGRALEQUATIONFREDHOLMFINALVERSION12
download (TrueBasic,outp1) :INTERGRALEQUATIONFREDHOLMFINALVERSION12outp
download (TrueBasic,code) :INTERGRALEQUATIONFREDHOLMFINALVERSION20final
download (TrueBasic,outp1) :INTERGRALEQUATIONFREDHOLMFINALVERSION20finaloutp
download (TrueBasic,code) :INTERGRALEQUATIONFREDHOLMFINALVERSION21final
download (TrueBasic,outp1) :INTERGRALEQUATIONFREDHOLMFINALVERSION21finaloutp
download (TrueBasic,outpex) :intergralequationfredholmfinalversion11outptheory
download (TrueBasic,outpth) :intergralequationfredholmfinalversion20outptheory
download (Maxima,code) :infotheorymaximaintegralequation
download (Maxima,png) :infotheorymaximaintegralequationoutp
download (TrueBasic,code) :INTERGRALEQUATIONFREDHOLMFINALVERSION22finalsubversion,sub
download (TrueBasic,outp1) :INTERGRALEQUATIONFREDHOLMFINALVERSION22finalsubversionoutp,sub
download (TrueBasic,code) :INTERGRALEQUATIONFREDHOLMFINALVERSION23FINALSUBVERSION,sub
download (TrueBasic,outp1) :INTERGRALEQUATIONFREDHOLMFINALVERSION23FINALSUBVERSIONoutp1,sub
download (TrueBasic,outp2) :INTERGRALEQUATIONFREDHOLMFINALVERSION23FINALSUBVERSIONoutp2,sub
download (TrueBasic,outp3) :INTERGRALEQUATIONFREDHOLMFINALVERSION23FINALSUBVERSIONoutp3,sub
2e) orthogonal collocation method
------------------------------------------------------
new: 03/09/2019:ortho collocation method : shifted legendre polynomials, 'version 1.0',part 1
download (Maxima,code) :orthocolshiftedlegendrepolynomialszeroto1version1finalpart1
download (Maxima,png) :orthocolshiftedlegendrepolynomialszeroto1version1finalpart1outp
new: 17/09/2019:ortho collocation method : shifted legendre polynomials, 'version 1.0',part 2
download (Maxima,code) :orthocolshiftedlegendredifferentialeqversion1finalpart2
download (Maxima,png) :orthocolshiftedlegendredifferentialeqversion1finalpart2outp
new: 17/09/2019:ortho collocation method : shifted legendre polynomials (hypergeometric :2F1), 'version 1.0',part3
download (Maxima,code) :orthocolshiftedlegendredifferentialeqversion1finalpart3
download (Maxima,png) :orthocolshiftedlegendredifferentialeqversion1finalpart3outp
new: 09/11/2020:maxima : appendix : 'ortho collocation method :sum,legendre',version 1.0
download (Maxima,code) :maximaappendixorthocollocationsumlegversion1final
download (Maxima,png) :maximaappendixorthocollocationsumlegversion1finaloutp
new: 16/11/2020:maxima : point collocation method,version 1.0,part 1
download (Maxima,code) :maximapointcollocationversion1finalpart1
download (Maxima,png) :maximapointcollocationversion1finalpart1outp
new: 17/11/2020:maxima : point collocation method,version 1.0,part 2
download (Maxima,code) :maximapointcollocationversion1finalpart2
download (Maxima,png) :maximapointcollocationversion1finalpart2outp
new: 27/11/2020:maxima : orthogonal collocation BVP :ODE,c(x) ,iso TRAM, vesion 1.0
youtube :Orthogonal Collocations Method for Solving ODE - BVPs and PDEs
download (Maxima,code) :maximaorthocollocisotramversion1final
download (Maxima,png) :maximaorthocollocisotramversion1finaloutp
new: 01/12/2020:maxima : orthogonal collocation BVP :PDE c(x,t),iso TRAM, version 1.0
download (Maxima,code) :maximaorthocollocpdetimeisotramversion1final
download (Maxima,png) :maximaorthocollocpdetimeisotramversion1finaloutp
problem :
new: 17/11/2020:maxima :modified TRAM ODE-BVP problem ,version 1,part 1
download (Maxima,code) :maximamodifiedTRAMODEBVPversion1finalpart1
download (Maxima,png) :maximamodifiedTRAMODEBVPversion1finalpart1outp
new: 17/11/2020:maxima :appendix modified TRAM ODE-BVP problem ,version 1.
download (Maxima,code) :appendixmodifiedTRAMODEBVPversion1final
download (Maxima,png) :appendixmodifiedTRAMODEBVPversion1finaloutp
new: 25/11/2020:maxima : Tram (= finite difference), with irreversible sec order reaction,version 1.0
download (Maxima,code) :maximafinitediftramsecorderversion1final
download (Maxima,png) :maximafinitediftramsecorderversion1finaloutp
new: 19/11/2020:maxima :polynoom operation,translation version 1.0a
ref :https://www.youtube.com/watch?v=KhxiBgNfPBg
download (Maxima,code) :maximatranslatepolynoomvesrsion1
download (Maxima,png) :maximatranslatepolynoomvesrsion1outp
download (Maxima,code) :maximatranslatepolynoomvesrsion1a
download (Maxima,png) :maximatranslatepolynoomvesrsion1aoutp
new: 20/11/2020:maxima:Gram-Schmidt Process ,orthogonal system,version 1.0.
ref :youtube :
→ https://www.youtube.com/watch?v=nAR0enu6X24
→https://www.youtube.com/watch?v=uMGRiifW1KY&t=103s
→ https://www.youtube.com/watch?v=mj1kVkzByko&t=24s
https://www.youtube.com/watch?v=zHbfZWZJTGc&t=435s
download (Maxima,code) :maximagramschmidtorthogonalizationversion1
download (Maxima,png) :maximagramschmidtorthogonalizationversion1outp
new:06/12/2020: maxima: backsubst ( = list structure),version 1.0
download (Maxima,code) :maximabacksubstofliststructureversion1final
download (Maxima,png) :maximabacksubstofliststructureversion1finaloutp
new:09/12/2020: maxima :orthogonality fourier series ,version 1.0
download (Maxima,code) :maximaorthogonalityfourierseriesheatversion1
download (Maxima,png) :maximaorthogonalityfourierseriesheatversion1outp
appendix :
new:13/12/2020: maxima:appendix : intersection between two function , version 1.0
download (Maxima,code) :appendixintersectwocurveversion1final
download (Maxima,png) :appendixintersectwocurveversion1finaloutp
3e) numerical methods(pde)
---------------------------------------------
see : 'above'
4e) perturbation methods
-----------------------------------------
new: 02/03/2020:Introduction to perturbations , version 1.0
download (Maxima,code) :maximaispecialntroductiontopertubtheoryversion1
download (Maxima,png) :maximaispecialntroductiontopertubtheoryversion1outp
new: 03/03/2020:appendix :perturbation ,linear inhomogeneous diff eq,variation of parameters,version 1
download (Maxima,code) :appendixlininhomogodevariationparversion1
download (Maxima,png) :appendixlininhomogodevariationparversion1outp
new: 03/03/2020:appendix :example :f(x),variation parameter f(x) = tan(x),version 1.0
download (Maxima,code) :maximavariationmethodextanxversion1
download (Maxima,png) :maximavariationmethodextanxversion1outp
new: 05/03/2020:maxima:special:perturbation (=second order,nonlinear bvp),version 1.0,part1
download (Maxima,code) :maximaspecialperturbodesversion1finalpart1
download (Maxima,png) :maximaspecialperturbodesversion1finalpart1outp
new: 05/03/2020: example :variation parameter f(x) =perturb example,version 1.0,part2
download (Maxima,code) :maximavariationmethodextanxversion1testexamplepart2
download (Maxima,png) :maximavariationmethodextanxversion1testexamplepart2outp
new: 15 /03/2020:appendix : a(x),b(x),simple result,version 1.0,part 3
download (Maxima,code) :appendixaxbxsimpleresultversion1finalpart3
download (Maxima,png) :appendixaxbxsimpleresultversion1finalpart3outp
new: ? /03/2020:********** :*******************************************************
download (Maxima,code) :
download (Maxima,png) :
5e) value : infinite sum (use :hypergeometric series,gamma function....)
-----------------------------------------
new: 08 /12/2020:maxima:sum infinity ( = value ?),version 1.0,part 1
download (Maxima,code) :maximainfinitysumpart1version1final
download (Maxima,png) :maximainfinitysumpart1version1finaloutp
new: 08 /12/2020:maxima:sum infinity ( = value ?),version 1.0,part 2
download (Maxima,code) :maximainfinitysumpart2version1final
download (Maxima,png) :maximainfinitysumpart2version1finaloutp
new: 08/12/2020:maxima:sum infinity ( = value ?),version 1.0,part 3
download (Maxima,code) :maximainfinitysumpart3version1final
download (Maxima,png) :pmaximainfinitysumpart3version1finaloutp
new: 08/12/2020:maxima:sum infinity ( = value ?),version 1.0,part 4
download (Maxima,code) :maximainfinitysumpart4version1final
download (Maxima,png) :maximainfinitysumpart4version1finaloutp
new: 08/12/2020:maxima:sum infinity ( = value ?),version 1.0,part 5
download (Maxima,code) :maximainfinitysumpart5version1final
download (Maxima,png) :maximainfinitysumpart5version1finaloutp
6e) value : first order linear pde (use :construct,theory,pP+qQ=R.......)
------------------------------------------------
new: 01/05/2021: maxima :intro how construct pde from geometrical shape (p,q),version1,part 1.
download (Maxima,code) :maximageomconstructpdepart1version1
download (Maxima,png) :maximageomconstructpdepart1version1outp
new: 01/05/2021: maxima :how construct pde(p,q) :eliminating arbitrary (a,b),version1,part 2.
download (Maxima,code) :maximageomconstructpdepart2version1
download (Maxima,png) :maximageomconstructpdepart2version1outp
new: 01/05/2021: maxima :intro how construct pde from geometrical shape (p,q,r,s,t),version1,part 3.
download (Maxima,code) :maximageomconstructpdepart3version1
download (Maxima,png) :maximageomconstructpdepart3version1outp
new: 01/05/2021: maxima :intro how construct pde from arbitrary functions version1,part 4.
download (Maxima,code) :maximageomconstructpdepart4version1
download (Maxima,png) :maximageomconstructpdepart4version1outp
new: 03/05/2021: maxima :intro how construct pde complex theory version1,part 5a.
download (Maxima,code) :maximageomconstructpdepart5aversion1
download (Maxima,png) :maximageomconstructpdepart5aversion1outp
new: 03/05/2021: maxima :intro how construct first order pde theory (version1),part 5b.
download (Maxima,code) :maximageomconstructpdepart5bversion1
download (Maxima,png) :maximageomconstructpdepart5bversion1outp
new: 03/05/2021: maxima :intro how construct first order pde theory (version1),part 5c
download (Maxima,code) :maximageomconstructpdepart5cversion1
download (Maxima,png) :maximageomconstructpdepart5cversion1outp
new: 03/05/2021: maxima :intro how construct first order pde origin (version1),part 5d
download (Maxima,code) :maximageomconstructpdepart5dversion1
download (Maxima,png) maximageomconstructpdepart5dversion1outp
(appendix)
new: 17/05/2021: appendix1 : intro 1e order pde : functions (functions) & derivatives,version1.0
download (Maxima,code) :maximaapp1firstorderderrivativeandfunctionversion12021
download (Maxima,png) :maximaapp1firstorderderrivativeandfunctionversion12021outp
new: 18/05/2021: appendix1 : intro 1e order pde : functions (functions) & derivatives,version1.0a
download (Maxima,code) :maximaapp1firstorderderrivativeandfunctionversion1a2021
download (Maxima,png) :maximaapp1firstorderderrivativeandfunctionversion1a2021outp
(examples)
new: 29/08/2021:maxima :first order pde for problem of the plane.
download (Maxima,code) :maximafirstorderpdeproblemoftheplaneversion12021
download (Maxima,png) : maximafirstorderpdeproblemoftheplaneversion12021outp
7e) other methods( = finite element)
-----------------------------
new: 15/12/2020:maxima: Weighted residual methods,version 1.0
ref :https://www.youtube.com/watch?v=M2AwacE25iI&list=PLVLLmrCGvV_zgEABjq4JCRK9B25imxt6S&index=14
first method : Least Square Method (LSM)
second method : Point Collocation Method (PCM)
third method : Sub Domain Method (SDM)
fourth method : Galerkin Method (GM), Best Method (see :wxplot2d)
download (Maxima,code) :maximadeweghtedresidualmethodsversion1final
download (Maxima,png) :maximadeweghtedresidualmethodsversion1finaloutp
new: 17/12/2020:maxima : brachistochron problem,version 1.0
Euler Lagrange Equation (optimize)
download (Maxima,code) :maximabrachistochronproblemversion1final
download (Maxima,png) :maximabrachistochronproblemversion1finaloutp
new: 20/12/2020:maxima :apply general BC on a stiff system ( 'finite element'),version 1.0
download (Maxima,code) :maximageneralbcappliedtomodelfiniteelmementversion1
download (Maxima,png) :maximageneralbcappliedtomodelfiniteelmementversion1outp
new: 23/12/2020:maxima :method :undetermined coefficients, integration,version 1.0
download (Maxima,code) :maximamethodundeterminedintgversion1final
download (Maxima,png) :maximamethodundeterminedintgversion1finaloutp
new: 24/12/2020:maxima:gauss-legendre quadrature, integration,version 1.0
download (Maxima,code) :maximagausslegendrequadraturetwopointformulaversion1
download (Maxima,png) :maximagausslegendrequadraturetwopointformulaversion1outp
new: 26/12/2020:maxima:introduction to chebyshev :polynomials,version 1.0
download (Maxima,code) :maximaintrochebyshevpolynversion1final
download (Maxima,png) :maximaintrochebyshevpolynversion1finaloutp
new: 03/01/2021:maxima:i finite element (=discrete), version 1.0,part 1
download (Maxima,code) :maximafinelemdiscreetversion1final2021part1
download (Maxima,code) :maximafinelemdiscreetversion1final2021part1outp
new: 04/01/2021:maxima:ifinite element (=discrete), version 1.0,part 2
download (Maxima,code) :maximafinelemdiscreetversion1final2021part2
download (Maxima,code) :maximafinelemdiscreetversion1final2021part2outp
appendix:
new: 04 /01/2021:maxima: relation between fft & inverse_fft ,version 1.0
download (Maxima,code) :maximabasicfftandinverseifftversion1
download (Maxima,png) :maximabasicfftandinverseifftversion1outp
new: 06 /01/2021:maxima: relation between fft & inverse_fft (1D,2D),version 1.0a
download (Maxima,code) :maximabasicfftandinverseifftversion1a
download (Maxima,png) :maximabasicfftandinverseifftversion1aoutp
new: 13 /01/2021:maxima : approximation 1e order differentation f(x) = f'(x) with fft,version 1.0
download (Maxima,code) :maxidifferentationapproxwithfftversion1final
download (Maxima,png) :maxidifferentationapproxwithfftversion1finaloutp
new: 14 /01/2021:maxima : discrete fourier transform 'gauss function',differentation,version 1.0
download (Maxima,code) :maximadiscreteftransgaussdiffversion1final
download (Maxima,png) :maximadiscreteftransgaussdiffversion1finaloutp
ref : Maple Code
download (Maple ,code) :prof Denis Constales UGent ,petermacfft
appendix : complex variable ( = solve pde,ode)
========================================
1e) inverse laplace transform, residue theorem.
--------------------------------------------------------------------------
new:31/07/2019:complex:appendix:How to find :inverse laplace transform(=ilt)
download (Maxima,code) :appendixinverselaplacetransversion1final
download (Maxima,png) :appendixinverselaplacetransversion1finaloutp
2e) inverse laplace transform, f(s),poles,essential singularities.
-------------------------------------------------------------------------------------------------
new:04/08/2019:complex:essential singularities @ poles ,f(s) example , version 1
use :sinh(i*x) =i*sin(x),cosh(i*x) = cos(x) , 0/0 = infinity/infinity = l'hopital rule.
download (Maxima,code) :complexvarexample1invlaplasingularityversion1
download (Maxima,png) :complexvarexample1invlaplasingularityversion1outp
3e) inverse laplace transform,'relation with fourier transform'
-------------------------------------------------------------------------------------------------
new:04/08/2019:complex:relation between : inverse laplace transform & fourier transform,version 1.0
download (Maxima,code) :complexrelationbetweeniltandfouriertrformversion1
download (Maxima,png) :complexrelationbetweeniltandfouriertrformversion1outp
4e) hulp integration ( list & integral)
--------------------------------------------------------
new:04/08/2019:complex:principal: relation integration and list parameters from integration,version 1.0
download (Maxima,code) :hulpchangeintegrationinputversion1
download (Maxima,png) :hulpchangeintegrationinputversion1outp
5e) proof:jordan's lemma
--------------------------------------------------------
new:06/08/2019:complex:proof : jordan's lemma (inverse laplace transform = 'ilt'),version 1.0
download (Maxima,code) :proofjordanlemmainvlaplaceversion1final
download (Maxima,png) :proofjordanlemmainvlaplaceversion1finaloutp
6e) integration by parts (derivatives, laplace transform & fourier transform), 'correction'
-------------------------------------------------------------------------------------------------------------------------
new:09/08/2019:complex:integration by parts : laplace transform,fourier transform (second derivative), version 1.0a
download (Maxima,code) :integrationbypartsfouriertrlaplacetrofsecderivativeversion1afinal
download (Maxima,png) :integrationbypartsfouriertrlaplacetrofsecderivativeversion1afinaloutp
appendix :
new:09/08/2019:complex:appendix ('nth order derivative,laplace transform'),version 1.0
download (Maxima,code) :icomplexappendixlaplacetrnorderderversion1final
download (Maxima,png) complexappendixlaplacetrnorderderversion1finaloutp
biotech:covid-19,vectorfield,casino (2022)
___________________________________________________
BIOTECH :COVID-19 (RO=2.68) :" SIR model:math".' simulation,prediction
================================================================
Multi-compartment model ( = epidemics), intro to reaction engineering.
new: 21/04/2020:maxima : biotech : numerical model (rk4),epidemic: one ode, version 1.0a.
download (Maxima,code) :biotechsimplemepidemicnumrk4version1final1a
download (Maxima,png) :biotechsimplemepidemicnumrk4version1final1aoutp
new: 21/04/2020:maxima : biotech : S,I incomplete model,used phase analysis,version 1.0
download (Maxima,code) :biotechincompleteSIphaseplaneversion1plotdf4
download (Maxima,png) :biotechincompletesiphaseplaneversion1plotdf4outp
new: 21/04/2020:maxima : biotech : S,I ,R complete model,version 1.0
download (Maxima,code) :biotechSIRcompletemodelversion1finalfinalfinalfinal
download (Maxima,png) :biotechSIRcompletemodelversion1finalfinalfinalfinaloutp
new: 21/04/2020:maxima : biotech : appendix parameter μ,β (SIR model),version 1.0
(info : medical journal :lancet,RO = 2.68,td= 6.4 days ,doubling time ,china)
download (Maxima,code) :biotechparameterbetamulancetversion1final
download (Maxima,png) :biotechparameterbetamulancetversion1finaloutp
new: 24/04/2020:maxima : biotech : algo 'euler method': (spreadsheet,sir math model)
download (openoffice.code) :calctest
new: 01/05/2020:maxima : biotech : S,I ,R (+Diffusion) =travelling wave model,version 1.0
download (Maxima,code) :biotechsirdiffusiontravelwaveversion1finalfinal
download (Maxima,png) :biotechsirdiffusiontravelwaveversion1finalfinaloutp
FISHER EQUATION = FE , nonlinear pde
new: 11/05/2020:maxima : biotech : Fisher Equation( = pde),intro (relation dimensional,non dimensional) ,version 1.0
download (Maxima,code) :biotechfishereqpdeintroversion1final
download (Maxima,png) :biotechfishereqpdeintroversion1finaloutp
new: 11/05/2020:maxima : biotech : Fisher Equation( = pde),travelling wave propagation :part 1,version 1.0
download (Maxima,code) :biotechfepdetravelpart1version1final
download (Maxima,png) :biotechfepdetravelpart1version1finaloutp
new: 11/05/2020:maxima : biotech : Fisher Equation( = pde),phase plane analysis :part 2,version 1.0
download (Maxima,code) :biotechfepdephaseplanepart2version1final
download (Maxima,png) :biotechfepdephaseplanepart2version1finaloutp
new: 13/05/2020:maxima : biotech : Fisher Equation( = pde),find U(z) ? , wavefront propagation from FE :part 3,version 1.0
download (Maxima,code) :biotechuzfromfepart3version1finalfinal
download (Maxima,png) :biotechuzfromfepart3version1finalfinaloutp
new: 14/05/2020:maxima : biotech : U(z) = one term approx,wavefront propagation FE ,part 4,vesion1.0
download (Maxima,code) :biotechuzfromfepart4version1final
download (Maxima,png) :biotechuzfromfepart4version1finaloutp
Numerical : 'multiplot: Maxima'
new: 20/05/2020:maxima : biotech : numerical simple diffusion pde ,version 1.0
download (Maxima,code) :biotechnumericaldiffusionpdeversion1final
download (Maxima,png) :biotechnumericaldiffusionpdeversion1finaloutp
new: 24/05/2020:maxima : biotech : advection equation, upwind scheme,version 1.0
download (Maxima,code) :biotechadvupwindinitshapeversion1final
download (Maxima,png) :biotechadvupwindinitshapeversion1finaloutp
new: 27/05/2020:maxima : biotech : method of lines 'fisher nonlinear pde', version 1.0
download (Maxima,code) :biotechsolvepdefisher molmethodversion1final
download (Maxima,png) :biotechsolvepdefisher molmethodversion1finaloutp
new: 27/05/2020:maxima : biotech : apppendix : method of lines 'fisher nonlinear pde', version 1
download (Maxima,code) :biotechappendixfisherdiscreteschememethodoflinesversion1final
download (Maxima,png) :biotechappendixfisherdiscreteschememethodoflinesversion1finaloutp
new: 08/05/2020:maxima : biotech :appendix 1: second order ode : coef D,c ,version 1.0
download (Maxima,code) :biotechappendixsecodedcversion1finalfinal
download (Maxima,png) :biotechappendixsecodedcversion1finalfinaloutp
new: 12/05/2020:maxima : biotech :appendix 1a: How to get ε second order diff equation from the travel wave propagation ,version1
download (Maxima,code) :biotechappendix1awavefrFetoepsilondiffeqversion1final
download (Maxima,png) :biotechappendix1awavefrfetoepsilondiffeqversion1finaloutp
new: 08/05/2020:maxima : biotech :appendix 2: asymptotic solution(second order diff. equation),version 1.0
download (Maxima,code) :biotechappendix2asympsecondorderdiffversion1final
download (Maxima,png) :biotechappendix2asympsecondorderdiffversion1finaloutp
new: 10/05/2020:maxima : biotech :appendix 3: limits of fisher equation (-∞,0,∞),version 1.0
download (Maxima,code) :biotechappendix3fisherpdelimitsversion1final
download (Maxima,png) :biotechappendix3fisherpdelimitsversion1finaloutp
vector field (2D-3D), truebasic (plot) & Maxima(plot)
===========================================
programming : general
new: 29/04/2020:vector field 2D
download (Truebasic ,code ):VECTORFIELD2DFINALVERSION1
download (TrueBasic,outp ):VECTORFIELD2DFINALVERSION1outp
new: 10/10/2020:truebasic : vector field 2d : with trajectory , version 1.0
download (Truebasic ,code ):vectorfield2dwithtrajectfinalversion1
download (TrueBasic,outp ):vectorfield2dwithtrajectfinalversion1outp
new: 20/10/2020:maxima : vector field 2d : with trajectory , version 1.0b
download (Maxima,code) :maxtruevectorfield2dversion1trajectoryfinal
download (Maxima,png) :maxtruevectorfield2dversion1trajectoryfinaloutp
download (Maxima,code) :vectorfield2dwithtrajectfinalversion1a
download (Maxima,png) :vectorfield2dwithtrajectfinalversion1aoutp
download (Maxima,code) :maxtruevectorfield2dversion1btrajectoryfinal
download (Maxima,png) :maxtruevectorfield2dversion1btrajectoryfinaloutp
new: 11/01/2021:maxima : vector field 2d : with arrows , version 1.0
download (Truebasic ,code ):TRUEBASIC2DVECTORFIELDWITHARROWSVERSION12021
download (TrueBasic,outp ):TRUEBASIC2DVECTORFIELDWITHARROWSVERSION1202outp
new: 18/01/2021:maxima : vector field 2d : with arrows ,trajectory version 1.0
download (Truebasic ,code ):TRUEBASIC2DVECTORFIELDWITHARROWSVERSION12021trajectfinal
download (TrueBasic,outp ):TRUEBASIC2DVECTORFIELDWITHARROWSVERSION12021trajectfinaloutp
new: 19/01/2021:maxima : vector field 2d : with arrows ,trajectory,aspectratio version 1.0a,optimized
download (Truebasic ,code ):TRUEBASIC2DVECTORFIELDWITHARROWSVERSION12021TRAJECTaspectratioFINAL1a
download (Truebasic ,code ):TRUEBASIC2DVECTORFIELDWITHARROWSVERSION12021TRAJECTaspectratioFINAL1aoutp
new: 21/01/2021:truebasic :vector field 2d:with arrows,trajectory,aspectratio,sub version 1.0b
download (Truebasic ,code ):TRUEBASIC2DVECTORFIELDWITHARROWSVERSION12021TRAJECTASPECTRATIOFINAL1B
download (Truebasic ,code ):TRUEBASIC2DVECTORFIELDWITHARROWSVERSION12021TRAJECTASPECTRATIOFINAL1Boutp
new: 29/04/2020:vector field 3D ,version 1.0
download (Truebasic ,code ):VECTORFIELD3D07042020UPDATE
download (TrueBasic,outp ):VECTORFIELD3D07042020UPDATEoutp
new: 18/10/2020:truebasic : vector field 3d : with trajectory , version 1.0b
download (Truebasic ,code ):TRUEVECTORFIELD3DWITHTRAJECTORYVERSION1A
download (Truebasic ,outp ):TRUEVECTORFIELD3DWITHTRAJECTORYVERSION1Aoutp
download (Truebasic ,code ):TRUEVECTORFIELD3DWITHTRAJECTORYVERSION1B
download (Truebasic ,code ):TRUEVECTORFIELD3DWITHTRAJECTORYVERSION1Boutp
Plot vector Field 2d,3d 'maxima', commands 'Maxima'
============================================
programming : Maxima
new: 04/04/2020:Plot : maxima:vector field (2d:F:<,>,3d:F:<,,>),version 1.0
download (Maxima,code) :maximaplotvecfield2d3dversion1final
download (Maxima,png) :maximaplotvecfield2d3dversion1finaloutp.png
new: 04/04/2020:Plot : maxima : plot with definitions of 2d vector field,version 1.0
download (Maxima,code) :maximaplotwithdeftwovecfieldversion1final
download (Maxima,png) :maximaplotwithdeftwovecfieldversion1finaloutp
new: 04/04/2020:Plot : maxima : plot with definitions of 3d vector field,version 1.0
download (Maxima,code) :maximaplotwithdefthreevecfieldversion1final
download (Maxima,png) :maximaplotwithdefthreevecfieldversion1finaloutp
Casino :" Why play or not".
=======================
youtube :ref :https://www.youtube.com/watch?v=9FVlkg2bLlI
new: 02/02/2020:maxima : casino ( Why play or not: random walk),version 1.0,part 1
=> how to use the packages : solve_rec ( = first order: Difference equation,
a1*a[n+1] +a0*a[n] =0 )
download (Maxima,code) :maximacasinordnwalkversion1finalpart1
download (Maxima,png) :maximacasinordnwalkversion1finalpart1outp
new: 02/02/2020:maxima : casino ( Why play or not: random walk),version 1.0,part 2
=> how to use the packages : solve_rec ( = second order: Difference equation,
a2*a[n+2]+a1*a[n+1] + a0*a[n] =0)
download (Maxima,code) :maximacasinordnwalkversion1finalpart2
download (Maxima,png) :maximacasinordnwalkversion1finalpart2outp
new: 03/02/2020:maxima : casino ( Why play or not: random walk),version 1.0,part 3
download (Maxima,code) :maximacasinordnwalkversion1finalpart3
download (Maxima,png) :maximacasinordnwalkversion1finalpart3outp