PK heQBH mimetypetext/x-wxmathmlPK heQQdBV5 5
format.txt
This file contains a wxMaxima session in the .wxmx format.
.wxmx files are .xml-based files contained in a .zip container like .odt
or .docx files. After changing their name to end in .zip the .xml and
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viewer.
The reason why part of a .wxmx file still might still seem to make sense in a
ordinary text viewer is that the text portion of .wxmx by default
isn't compressed: The text is typically small and compressing it would
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wxMaxima can be downloaded from https://github.com/wxMaxima-developers/wxmaxima.
It also is part of the windows installer for maxima
(https://wxmaxima-developers.github.io/wxmaxima/).
If a .wxmx file is broken but the content.xml portion of the file can still be
viewed using an text editor just save the xml's text as "content.xml"
and try to open it using a recent version of wxMaxima.
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the text is saved with the text encoding "UTF8 without BOM" and the few
special characters XML requires this for are properly escaped)
chances are high that wxMaxima will be able to recover all code and text
from the XML file.
PK heQ content.xml
Cálculo diferencial en varias variablesMini intro2+2; 3-3; 2*3; 5/10; 3^3;e;float(e);float(2); %e;float(%e);(2+3^2)^3*(5+2^2); x:123; y:321; z=2;z;x; y;x*y;x+z;x+y;%*10; f(x):= x^2 -x + 1;f(x);f(z);f(%pi); float(f(%pi));??float;??renato;/* MANUAL ONLINE */; wxplot2d([f(x)], [x,-5,5]);x;wxplot2d([f(s)], [s,-5,5]);kill(x);wxplot2d([f(x)], [x,-5,5]);plot2d( [ f(x) , 2*sin(x) , atan(x) ] , [x,-2,2])$log(10);float(%);log(%e); 15!; factor(%);Resolviendo ecuacioneskill(all)$solve( x^2-a=4 ,x);solve(x^2-a-4=0,x);solve(x^2-a-4,a); solve(x^2=-1); solve(x^5=1,x); solve(x^n=1,x);kk:7$ /* probar con 4,5,6,7, ....*/solve(x^kk=1,x); polarform(%);Límites de una variablesin(a*x)/x;limit(sin(a*x)/x,x,0);limit(exp(1/(1-x)),x,1);??und;exp(1/(1-x)); limit(exp(1/(1-x)),x,1,plus); limit(exp(1/(1-x)),x,1,minus); limit(log(x),x,0);f(x,y):=(x*y)/(x^2+y^2);limit(f(x,y),x,0); limit(f(x,y),y,0);limit(f(x,m*x),x,0); f(x,y):=(x^2*y)/(x^2+y^2);limit(f(x,m*x),x,0); limit(f(x,m*x^4),x,0); limit(f(x,sqrt(x)),x,0); Derivadasdiff( sin(x^2+2) , x ,3 );diff(x^x, x , 3);ratsimp(%);factor(%);f(x,y);diff(f(x,y), x);ratsimp(%);factor(%);diff(f(x,y), y);factor(%);diff(f(x,y));Dibujando en 3Dkill(f,x,y)$f(x,y):= sin(x) + cos(y);wxplot3d( f(x,y) , [x,-5,5] , [y,-5,5] )$plot3d(f(x,y), [x,-5,5], [y,-5,5])$load(draw)$wxdraw3d( proportional_axes = 'xyz, color=blue, xu_grid = 50, explicit(f(x,y), x,-5,5,y,-5,5) )$draw3d( proportional_axes = 'xyz, color=red, xu_grid = 10, explicit(f(x,y), x,-5,5,y,-5,5) )$draw3d( proportional_axes = 'xyz, color=cyan, xu_grid =50, explicit(f(x,y), x,-5,5,y,-5,5), point_type=filled_circle, point_size =2,color = blue, points([[2,1,f(2,1)]]))$Límites, continuidad y diferenciabilidadEjemplo 1kill(f)$f(x,y):=if x^2+y^2=0 then 0 else x*y/(y^2+x^2);f(2,1);f(0,0);/* Dibujamos la función */draw3d(enhanced3d = false, xu_grid = 100, color = gray50,explicit(f(x,y), x,-.1,.1,y,-.1,.1),point_type=filled_circle, point_size =2,color = black,points([[0,0,0]]) )$plot3d(f(x,y), [x,-.5,.5], [y,-.5,.5], [grid,80,80],[gnuplot_pm3d,true])$wxplot3d (5*f(x,y), [x,-.5,+.5], [y,-.5,+.5], [zlabel,""],[mesh_lines_color,false], [elevation,0], [azimuth,0],color_bar, [grid,80,80], [ztics,false], [color_bar_tics,1])$f(x,m*x);ratsimp(%);limit(f(x,m*x),x,0); /* Calculamos las derivadas parciales */diff(f(x,y),x);ratsimp(%);factor(%);ratsimp(diff(f(x,y),x)),factor;ratsimp(diff(f(x,y),y)),factor;ratsimp(f(x,0)/x);ratsimp(f(0,y)/x);(f(x,0)-f(0,0))/x;Ejemplo 2kill(f)$f(x,y):=if x^2+y^2=0 then 0 else x^2*y^2/(x^2+y^2) ;/* Dibujamos la función */draw3d ( enhanced3d = false, xu_grid = 50, color =grey50,explicit(f(x,y), x,-1,1,y,-1,1),point_type=filled_circle, point_size = 2,color = black,points([[0,0,0]]) )$f(x,m*x);ratsimp(%);limit(f(x,m*x),x,0); f(x,m*x^2), ratsimp; limit(f(x,m*x),x,0); f(x,m*x^(1/2)), ratsimp;limit(f(x,m*x),x,0); /* Calculamos las derivadas parciales */ratsimp(diff(f(x,y),x));ratsimp(diff(f(x,y),y));factor(%);/* Derivadas parciales el (0,0) */ratsimp(f(x,0)/x); ratsimp(f(0,y)/x);f(x,y)/sqrt(x^2+y^2);/* Diferenciabilidad */ draw3d ( enhanced3d = false, xu_grid = 50, color = red, explicit(f(x,y)/sqrt(x^2+y^2), x,-0.1,0.1,y,-0.1,0.1), point_type=filled_circle, point_size = 2,color = black, points([[0,0,0]]) )$g(x,y):=f(x,y)/sqrt(x^2+y^2);g(x,m*x);ratsimp(%);limit(g(x,m*x),x,0);g(x,m*x^2);ratsimp(%);radcan(%);limit(g(x,m*x^2),x,0);gra:ratsimp( jacobian([f(x,y)],[x,y]) );Ejemplo 3kill(g)$g(x,y):=if x^2+y^2=0 then 0 else atan((x^4+y^4)/(x^2+y^2));g(1,1);g(0,0);a:0$ b:0$g(x,y);g(x,m*x);ratsimp(%);limit(g(x,m*x),x,0);g(x,m*x^2), ratsimp;limit(g(x,m*x^2),x,0);g(x,m*x^(1/2)), ratsimp;limit(%,x,0);draw3d( enhanced3d = false, xu_grid = 50, color = cyan,explicit(g(x,y), x,-1,1,y,-1,1), point_type=filled_circle, point_size = 2,color = blue, points([[a,b,0]]) )$diff(g(x,y),x)$ ratsimp(%);diff(g(x,y),y)$ ratsimp(%);factor(%);g(x,0); g(0,y);/* Derivadas parciales el (0,0) */limit(g(x,0)/x,x,0);limit(g(0,y)/y,y,0);/* Dibujamos la función (Diferenciabilidad) */draw3d( enhanced3d = false, xu_grid = 50, color = red,explicit(g(x,y)/sqrt(x^2+y^2), x,-1,1,y,-1,1), point_type=filled_circle, point_size = 2,color = black, points([[a,b,0]]) )$ /* Dibujamos la función */ draw3d (enhanced3d = false, xu_grid = 50, color = red, explicit(g(x,y)/sqrt(x^2+y^2), x,-.1,.1,y,-.1,.1), point_type=filled_circle, point_size = 1,color = black, points([[0,0,0]]) )$gd(x,y):=g(x,y)/sqrt(x^2+y^2);gd(x,y);gd(x,m*x),ratsimp;limit(gd(x,m*x),x,0);gd(x,m*x^2),ratsimp;ratsimp(%);radcan(%);limit(gd(x,m*x^2),x,0);gd(x,m*sqrt(x) ),ratsimp;limit( gd(x, m*sqrt(x) ) , x, 0);Ejercicio kill(g)$g(x,y):=if x^2+y^2=0 then 0 else (x^2+y^2)*sin(1/sqrt(x^2+y^2));g(1,1);g(0,0);a:0$ b:0$g(x,y);g(x,m*x),ratsimp;limit(g(x,m*x),x,0);g(x,m*x^2), ratsimp;limit(g(x,m*x^2),x,0);g(x,m*x^(1/2)),ratsimp;limit(%,x,0);draw3d( enhanced3d = false, xu_grid = 50, color =dark_salmon,explicit(g(x,y), x,a-1/2,a+1/2,y,b-1/2,b+1/2), point_type=filled_circle, point_size =2,color = black, points([[a,b,0]]) )$draw3d( enhanced3d = false, xu_grid = 50, color = dark_salmon,explicit(g(x,y), x,a-.2,a+.2,y,b-.2,b+.2), point_type=filled_circle, point_size =2,color = black, points([[a,b,0]]) )$draw3d( enhanced3d = false, xu_grid = 50, color = dark_salmon,explicit(g(x,y), x,a-.1,a+.1,y,b-.1,b+.1), point_type=filled_circle, point_size =2,color = black, points([[a,b,0]]) )$diff(g(x,y),x)$ ratsimp(%);expand(%);diff(g(x,y),y)$ ratsimp(%);expand(%);g(x,0);g(0,y);limit(g(x,0)/x,x,0);limit(g(0,y)/y,y,0); g(x,y)/sqrt(x^2+y^2);/* Dibujamos la función (Diferenciabilidad) */draw3d( enhanced3d = false, xu_grid = 50, color = dark_salmon,explicit(g(x,y)/sqrt(x^2+y^2), x,a-2,a+2,y,b-2,b+2), point_type=filled_circle, point_size = 2,color = blue, points([[a,b,0]]) )$/* Dibujamos la función (Diferenciabilidad) */draw3d( enhanced3d = false, xu_grid = 50, color = dark_salmon,explicit(g(x,y)/sqrt(x^2+y^2), x,a-.2,a+.2,y,b-.2,b+.2), point_type=filled_circle, point_size =1,color = blue, points([[a,b,0]]) )$wxplot3d (50*g(x,y), [x,a-.1,a+.1], [y,a-.1,a+.1], [zlabel,""],[mesh_lines_color,false], [elevation,0], [azimuth,0],color_bar, [grid,80,80], [ztics,false], [color_bar_tics,1])$wxplot3d (10*g(x,y)/sqrt(x^2+y^2), [x,a-.1,a+.1], [y,a-.1,a+.1], [zlabel,""],[mesh_lines_color,false], [elevation,0], [azimuth,0],color_bar, [grid,80,80], [ztics,false], [color_bar_tics,1])$ Matrices JacobianasEjemplokill(f1,f2)$f1(x,y):= atan( (x+y)/(1-x*y) );f2(x,y):= tan(x^2/y);jacobian([f1(x,y),f2(x,y)],[x,y]);define(jac(x,y),ratsimp(%));jac(x,y);jac(%pi^(1/2),1);Ejerciciokill(f1,f2)$f1(x,y,z):= log(1+x^2+y^2+2*z^4);f2(x,y,z):= tanh(x^2-y*z);jacobian([f1(x,y,z),f2(x,y,z)],[x,y,z]);define(jac(x,y,z),ratsimp(%));jac(1,0,-1);float(%);jac(1,1,1);Calculando derivadas direccionales kill(all)$/* Definimos la norma en R^2 y R^3 */define(norm2(vv),sqrt(sum(vv[k]^2,k,1,2)));define(norm3(vv),sqrt(sum(vv[k]^2,k,1,3)));Ejemplo 1/* Definimos la funcion */ kill(f,a,b,c,v1,v2)$define(f(x,y),x^2*y^3);/* Calculamos las derivadas parciales */diff(f(x,y),x);diff(f(x,y),y);/* Calculamos el Jacobiano de la función */gra:jacobian([f(x,y)],[x,y]);/* Definimos el vector normalizado */v1:2$ v2:-1$ v:[v1,v2]$ vec:v/norm2(v);/* Calculamos la derivada direccional de f segun v y la evaluamos en (a,b) */a:1$ b:2$ c:f(a,b)$Du:gra.vec; /* Multiplicación de matrices */ev(Du,x=a,y=b);gra.vec;f(a,b); f(a+0.001*v1,b+0.001*v2);gra*vec;gra;vec;vec*vec;/* Dibujamos la función */draw3d( enhanced3d = false, xu_grid = 50, color = sea_green, explicit(f(x,y), x,a-2,a+2,y,b-2,b+2),point_type=filled_circle, point_size = 2,color = midnight_blue, points([[a,b,f(a,b)]]),head_angle = 20,head_length = 0.1,vector([a,b,c],[v1,v2,0]) )$Ejercicio 2/* EJEMPLO 3: Definimos la funcion */ kill(f,a,b,c,v1,v2)$define(f(x,y),sin( (x^2+y^2)/(x^2+y^2+1)));/* Calculamos las derivadas parciales */diff(f(x,y),x), ratsimp;diff(f(x,y),y), ratsimp;factor(%);/* Calculamos el Jacobiano de la función */gra:jacobian([f(x,y)],[x,y]),ratsimp;/* Definimos el vector normalizado */v1:-4$ v2:3$ v:[v1,v2]$ vec:v/norm2(v);/* Calculamos la derivada direccional de f segun v y la evaluamos en (a,b) */a:-1$ b:1$ c:f(a,b)$Du:gra.vec;ev(Du,x=a,y=b);float(%);/* Dibujamos la función */draw3d( enhanced3d = false, xu_grid = 50, color = spring_green,explicit(f(x,y), x,a-2,a+2,y,b-2,b+2),point_type=filled_circle, point_size = 2,color = forest_green, points([[a,b,f(a,b)]]),head_angle = 20,head_length = 0.1, vector([a,b,c],[v1,v2,0]) )$Ejercicio 3/* Definimos la funcion */kill(f,a,b,c)$define(f(x,y,z),(x/y)^z);gra:jacobian([f(x,y,z)],[x,y,z]);v:[2,1,-1]$ vec:v/norm3(v);a:%pi$ b:4$ c:2$ Du:gra.vec;ev(Du,x=a,y=b,z=c);float(%);Ejercicio 4/* Definimos la función */kill(f,a,b,c)$define(f(x,y),(x^2+y^2)^(x));gra:jacobian([f(x,y)],[x,y]);v1:1$ v2:-1$ v:[v1,v2]$ vec:v/norm2(v);a:%e$ b:0$ c:f(a,b)$Du:gra.vec;ev(Du,x=a,y=b);/* Dibujamos la función */draw3d( enhanced3d = false, xu_grid = 50, color = sea_green, explicit(f(x,y), x,a-1,a+1,y,b-1,b+1),point_type=filled_circle, point_size = 2,color = midnight_blue, points([[a,b,f(a,b)]]),head_angle = 20,head_length = 0.1, vector([a,b,c],[v1,v2,0]) )$Planos tangentesEjemplo 1kill(all)$es:1/5$define(f(x,y),es*(1-(x^2+y^2)));define(dxf(x,y),diff(f(x,y),x));define(dyf(x,y),diff(f(x,y),y));/* Ecuacion del plano */a:-1$ b:1$ c:f(a,b)$ xmin:a-1$ xmax:a+1$ ymin:b-1$ ymax:b+1$vn:[dxf(a,b),dyf(a,b),-1]*(-1);-z+f(a,b)+dxf(a,b)*(x-a)+dyf(a,b)*(y-b)=0;define(plano(x,y), f(a,b)+dxf(a,b)*(x-a)+dyf(a,b)*(y-b));draw3d( color=blue, xu_grid = 50, proportional_axes = 'xyz, explicit(f(x,y),x,xmin-1,xmax+1,y,ymin-1,ymax+1), color=cyan, parametric_surface(x,y,plano(x,y),x,xmin,xmax,y,ymin,ymax),point_type=filled_circle, point_size =2,color = black, points([[a,b,f(a,b)]]),head_angle = 20,head_length = 0.1,vector([a,b,c],vn) )$Ejercicio 1kill(all)$es:1/2$define(f(x,y),es*( x^2*y^2/(x^2+y^2) ));define(dxf(x,y),diff(f(x,y),x));define(dyf(x,y),diff(f(x,y),y));/* Ecuacion del plano */a:-2$ b:1$ c:f(a,b)$ xmin:a-1$ xmax:a+1$ ymin:b-1$ ymax:b+1$vn:[dxf(a,b),dyf(a,b),-1]*(1);z=f(a,b)+dxf(a,b)*(x-a)+dyf(a,b)*(y-b);define(plano(x,y), f(a,b)+dxf(a,b)*(x-a)+dyf(a,b)*(y-b));draw3d( color=blue, xu_grid = 50, explicit(f(x,y),x,xmin-1,xmax+1,y,ymin-1,ymax+1), color=cyan, parametric_surface(x,y,plano(x,y),x,xmin,xmax,y,ymin,ymax),point_type=filled_circle, point_size =1,color = black, points([[a,b,f(a,b)]]), head_angle = 20,head_length = 0.1,vector([a,b,c],vn) )$Ejercicio 2kill(all)$es:1$define(f(x,y),es*( atan(x^2+y^2) ));define(dxf(x,y),diff(f(x,y),x));define(dyf(x,y),diff(f(x,y),y));/* Ecuacion del plano */a:0$ b:1$ c:f(a,b)$ xmin:a-1$ xmax:a+1$ ymin:b-1$ ymax:b+1$vn:[dxf(a,b),dyf(a,b),-1]*(1);z=f(a,b)+dxf(a,b)*(x-a)+dyf(a,b)*(y-b);define(plano(x,y), f(a,b)+dxf(a,b)*(x-a)+dyf(a,b)*(y-b));draw3d( color=blue, xu_grid = 100, explicit(f(x,y),x,xmin-1,xmax+1,y,ymin-1,ymax+1),color=cyan, parametric_surface(x,y,plano(x,y),x,xmin,xmax,y,ymin,ymax),point_type=filled_circle, point_size =1,color = black, points([[a,b,f(a,b)]]),head_angle = 20,head_length = 0.1,vector([a,b,c],vn))$Ejercicio 3kill(all)$es:1/5$define(f(x,y),es*( (x^2+y^2)*sin((x^2+y^2)) ));define(dxf(x,y),diff(f(x,y),x));define(dyf(x,y),diff(f(x,y),y));/* Ecuacion del plano */a:0$ b:0$ c:f(a,b)$ xmin:a-1$ xmax:a+1$ ymin:b-1$ ymax:b+1$vn:[dxf(a,b),dyf(a,b),-1]*(-1);z=f(a,b)+dxf(a,b)*(x-a)+dyf(a,b)*(y-b);define(plano(x,y), f(a,b)+dxf(a,b)*(x-a)+dyf(a,b)*(y-b));draw3d( proportional_axes = 'xyz, color=blue, xu_grid = 50, explicit(f(x,y),x,xmin-1,xmax+1,y,ymin-1,ymax+1),color=red, parametric_surface(x,y,plano(x,y),x,xmin,xmax,y,ymin,ymax),point_type=filled_circle, point_size =1,color = black, points([[a,b,f(a,b)]]),head_angle = 20,head_length = 0.1,vector([a,b,c],vn))$a:1$ b:0$ c:f(a,b)$ xmin:a-1$ xmax:a+1$ ymin:b-1$ ymax:b+1$vn:[dxf(a,b),dyf(a,b),-1]*(-1);z=f(a,b)+dxf(a,b)*(x-a)+dyf(a,b)*(y-b);define(plano(x,y), f(a,b)+dxf(a,b)*(x-a)+dyf(a,b)*(y-b));draw3d( proportional_axes = 'xyz, color=blue, xu_grid = 50, explicit(f(x,y),x,xmin-1,xmax+1,y,ymin-1,ymax+1),color=red, parametric_surface(x,y,plano(x,y),x,xmin,xmax,y,ymin,ymax),point_type=filled_circle, point_size =1,color = black, points([[a,b,f(a,b)]]),head_angle = 20,head_length = 0.1,vector([a,b,c],vn))$Ejercicio 4kill(all)$es:2$define(f(x,y),es*( exp(-x^2-y^2) ));define(dxf(x,y),diff(f(x,y),x));define(dyf(x,y),diff(f(x,y),y));/* Ecuacion del plano */a:0$ b:0$ c:f(a,b)$ xmin:a-1$ xmax:a+1$ ymin:b-1$ ymax:b+1$vn:[dxf(a,b),dyf(a,b),-1]*(-1);z=f(a,b)+dxf(a,b)*(x-a)+dyf(a,b)*(y-b);define(plano(x,y), f(a,b)+dxf(a,b)*(x-a)+dyf(a,b)*(y-b));draw3d( proportional_axes = 'xyz, color=blue, xu_grid = 50, explicit(f(x,y),x,xmin-1,xmax+1,y,ymin-1,ymax+1),color=cyan, parametric_surface(x,y,plano(x,y),x,xmin,xmax,y,ymin,ymax),point_type=filled_circle, point_size =1,color = black, points([[a,b,f(a,b)]]),head_angle = 20,head_length = 0.1,vector([a,b,c],vn))$a:1/2$ b:-1/2$ c:f(a,b)$ xmin:a-1$ xmax:a+1$ ymin:b-1$ ymax:b+1$vn:[dxf(a,b),dyf(a,b),-1]*(-1);z=f(a,b)+dxf(a,b)*(x-a)+dyf(a,b)*(y-b);define(plano(x,y), f(a,b)+dxf(a,b)*(x-a)+dyf(a,b)*(y-b));draw3d( proportional_axes = 'xyz, color=blue, xu_grid = 50, explicit(f(x,y),x,xmin-1,xmax+1,y,ymin-1,ymax+1),color=red, parametric_surface(x,y,plano(x,y),x,xmin,xmax,y,ymin,ymax),point_type=filled_circle, point_size =1,color = black, points([[a,b,f(a,b)]]),head_angle = 20,head_length = 0.1,vector([a,b,c],vn) )$PK heQV ֦T T
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