4804.sagews

Vo=1
a=2
b=1
c=20
var('m')
T(x,y,m)=sin((2*m+1)*pi*x/a)*sinh((2*m+1)*pi*y/a)/((2*m+1)*sinh((2*m+1)*pi*b/a))
V(x,y)=4*Vo/pi*sum(T(x,y,m),m,0,10)
html('$V(x,y,z)= {4V_{0} \over \pi} \sum\limits_{m=0}^\infty%s$'%latex(T(x,y,m)))
contour_plot(V,(0,a),(0,b),cmap='Blues_r',contours=[Vo*t/c for t in range(0,c)],colorbar='true', linewidths=5,linestyles ='solid',axes_labels=['x','y'])

V(x,y,z)= {4V_{0} \over \pi} \sum\limits_{m=0}^\infty\frac{\sin\left(\frac{1}{2} \, {\left(2 \, m + 1\right)} \pi x\right) \sinh\left(\frac{1}{2} \, {\left(2 \, m + 1\right)} \pi y\right)}{{\left(2 \, m + 1\right)} \sinh\left(\frac{1}{2} \, {\left(2 \, m + 1\right)} \pi\right)}

html('$V(x,y,z)= {4V_{0} \over \pi} \sum\limits_{m=0}^\infty%s$'%latex(T(x,y,m)+T(x,b-y,m)))
contour_plot(V(x,y)+V(x,b-y),(x,0,a),(y,0,b),cmap='Blues_r',contours=[Vo*t/c for t in range(0,c)],colorbar='true', linewidths=5,linestyles ='solid',axes_labels=['x','y'])

V(x,y,z)= {4V_{0} \over \pi} \sum\limits_{m=0}^\infty\frac{\sin\left(\frac{1}{2} \, {\left(2 \, m + 1\right)} \pi x\right) \sinh\left(-\frac{1}{2} \, {\left(y - 1\right)} {\left(2 \, m + 1\right)} \pi\right)}{{\left(2 \, m + 1\right)} \sinh\left(\frac{1}{2} \, {\left(2 \, m + 1\right)} \pi\right)} + \frac{\sin\left(\frac{1}{2} \, {\left(2 \, m + 1\right)} \pi x\right) \sinh\left(\frac{1}{2} \, {\left(2 \, m + 1\right)} \pi y\right)}{{\left(2 \, m + 1\right)} \sinh\left(\frac{1}{2} \, {\left(2 \, m + 1\right)} \pi\right)}

html('$V(x,y,z)= {4V_{0} \over \pi} \sum\limits_{m=0}^\infty%s$'%latex(T(x,y,m)+T(a/b*y,b/a*x,m)))
contour_plot(V(x,y)+V(a/b*y,b/a*x),(x,0,a),(y,0,b),cmap='Blues_r',contours=[Vo*t/c for t in range(0,c)],colorbar='true', linewidths=5,linestyles ='solid',axes_labels=['x','y'])

V(x,y,z)= {4V_{0} \over \pi} \sum\limits_{m=0}^\infty\frac{\sin\left(\frac{1}{2} \, {\left(2 \, m + 1\right)} \pi x\right) \sinh\left(\frac{1}{2} \, {\left(2 \, m + 1\right)} \pi y\right)}{{\left(2 \, m + 1\right)} \sinh\left(\frac{1}{2} \, {\left(2 \, m + 1\right)} \pi\right)} + \frac{\sin\left({\left(2 \, m + 1\right)} \pi y\right) \sinh\left(\frac{1}{4} \, {\left(2 \, m + 1\right)} \pi x\right)}{{\left(2 \, m + 1\right)} \sinh\left(\frac{1}{2} \, {\left(2 \, m + 1\right)} \pi\right)}

contour_plot(V(x,y)+V((2*a)-x,y),(0,a),(0,b),cmap='Blues_r',contours=[Vo*t/c for t in range(0,c)],colorbar='true', linewidths=5,linestyles ='solid',axes_labels=['x','y'])