Heated rod with ice bath (Example 9.5.2) L := 50; u0:=100; k:=0.15;

IiNd

IiQrIg==

JCIjOiEiIw==

u := (x,t,N) -> (4*u0/Pi)* sum((1/(2*j-1)) * exp( -((2*j-1)*Pi/L)^2*k*t ) * sin((2*j-1)*Pi*x/L),j=1..N);

Zio2JUkieEc2IkkidEdGJUkiTkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCQqKEkjdTBHRiUiIiJJI1BpRyUqcHJvdGVjdGVkRyEiIi1JJHN1bUc2JEYwSShfc3lzbGliR0YlNiQqKCwmSSJqR0YlIiIjRjFGLkYxLUkkZXhwR0Y0NiMsJCosRjhGOkYvRjpJIkxHRiUhIiNJImtHRiVGLjklRi5GMUYuLUkkc2luR0Y0NiMqKkY4Ri5GL0YuOSRGLkZARjFGLi9GOTtGLjkmRi4iIiVGJUYlRiU=

plot3d(u(x,t,50),x=0..L,t=0..2000,color=black,style=wireframe,axes=boxed);

6'-%*AXESSTYLEG6#%$BOXG-%+AXESLABELSG6%Q"x6"Q"t6"Q!6"-%%GRIDG6&;$""!""!$"#]""!;$""!""!$"%+?""!X,I)anythingG%*protectedG6"6"[gl'!%"!!#\bm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

Heated rod with insulated ends (Example 9.5.3) f := x -> piecewise(0<x and x<=25, 4*x, 25<x and x<=50, 200-4*x);

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkqcGllY2V3aXNlRyUqcHJvdGVjdGVkRzYmMzIiIiE5JDFGMCIjRCwkRjAiIiUzMkYyRjAxRjAiI10sJiIkKyMiIiJGMCEiJUYlRiVGJQ==

plot(f(x),x=0..50, color=black);

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

Fourier series of f(t) a:= n-> (2/L) * int(f(x)*cos(n*Pi*x/L),x=0..L);

Zio2I0kibkc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCQqJkkiTEdGJSEiIi1JJGludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKiYtSSJmR0YlNiNJInhHRiUiIiItSSRjb3NHRi82IyoqOSRGOEkjUGlHRjBGOEY3RjhGK0YsRjgvRjc7IiIhRitGOCIiI0YlRiVGJQ==

f2 := (x,N) -> a(0)/2 + sum(a(n)*cos(n*Pi*x/L),n=1..N);

Zio2JEkieEc2IkkiTkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYtSSJhR0YlNiMiIiEjIiIiIiIjLUkkc3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQqJi1GLDYjSSJuR0YlRjAtSSRjb3NHRjQ2IyoqRjtGMEkjUGlHRjVGMDkkRjBJIkxHRiUhIiJGMC9GOztGMDklRjBGJUYlRiU=

plot({f2(x,10),f(x)},x=0..50);

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

u2 := (x,t,N) -> a(0)/2 + sum(a(n) * exp(-(n*Pi/L)^2*k*t) * cos(n*Pi*x/L),n=1..N);

Zio2JUkieEc2IkkidEdGJUkiTkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYtSSJhR0YlNiMiIiEjIiIiIiIjLUkkc3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQqKC1GLTYjSSJuR0YlRjEtSSRleHBHRjU2IywkKixGPEYySSNQaUdGNkYySSJMR0YlISIjSSJrR0YlRjE5JUYxISIiRjEtSSRjb3NHRjU2IyoqRjxGMUZCRjE5JEYxRkNGR0YxL0Y8O0YxOSZGMUYlRiVGJQ==

plot3d(u2(x,t,50),x=0..L,t=0..2000,color=black,style=wireframe,axes=boxed);

6'-%*AXESSTYLEG6#%$BOXG-%+AXESLABELSG6%Q"x6"Q"t6"Q!6"-%%GRIDG6&;$""!""!$"#]""!;$""!""!$"%+?""!X,I)anythingG%*protectedG6"6"[gl'!%"!!#\bm":":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%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%,ORIENTATIONG6$$"$I%!""$"$!e!""-%&STYLEG6#%%LINEG