# SECTION 7.6?Heavisideu := t -> Heaviside(t);

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plot(u,-2..2,scaling=constrained);

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plot(u(t-1),t=-2..2,scaling=constrained);

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

# Example 1f := 3*(1-u(t-2)) + 1*(u(t-2)-u(t-5)) + t*(u(t-5)-u(t-8)) + t^2/10*(u(t-8));

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plot(f,t=0..12,scaling=constrained);

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

?plot #Look up how to handle discontinuitiesplot(f,t=0..12,scaling=constrained,discont=true);

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

# Example 2with(inttrans);

NiM3LyUpYWRkdGFibGVHJShmb3VyaWVyRyUrZm91cmllcmNvc0clK2ZvdXJpZXJzaW5HJSdoYW5rZWxHJShoaWxiZXJ0RyUraW52Zm91cmllckclK2ludmhpbGJlcnRHJStpbnZsYXBsYWNlRyUqaW52bWVsbGluRyUobGFwbGFjZUclJ21lbGxpbkclKnNhdmV0YWJsZUc=

g := t -> t^2;

NiM+JSJnR2orNiMlInRHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0dGKCokKTkkIiIjIiIiRihGKEYoNiMiIiE=

a := 1;

NiM+JSJhRyIiIg==

g(t+a);

NiMqJCksJiUidEciIiJGJ0YnIiIjRic=

laplace(g(t+a),t,s);

NiMqJiwoIiIjIiIiKiZGJUYmJSJzR0YmRiYqJClGKEYlRiZGJkYmRighIiQ=

exp(-a*s)*laplace(g(t+a),t,s);

NiMqKC0lJGV4cEc2IywkJSJzRyEiIiIiIiwoIiIjRioqJkYsRipGKEYqRioqJClGKEYsRipGKkYqRighIiQ=

# Example 3g := t -> cos(t);

NiM+JSJnR2orNiMlInRHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0dGKC0lJGNvc0c2IzkkRihGKEYoNiMiIiE=

a := Pi;

NiM+JSJhRyUjUGlH

g(t+a);

NiMsJC0lJGNvc0c2IyUidEchIiI=

laplace(g(t+a),t,s);

NiMsJComJSJzRyIiIiwmKiQpRiUiIiNGJkYmRiZGJiEiIkYr

exp(-a*s)*laplace(g(t+a),t,s);

NiMsJCooLSUkZXhwRzYjLCQqJiUjUGlHIiIiJSJzR0YrISIiRitGLEYrLCYqJClGLCIiI0YrRitGK0YrRi1GLQ==

# Example 4F := 1/s^2;

NiM+JSJGRyomIiIiRiYqJCklInNHIiIjRiYhIiI=

a := 2;

NiM+JSJhRyIiIw==

invlaplace(F,s,t);

NiMlInRH

f := t -> t;

NiM+JSJmR2orNiMlInRHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0dGKDkkRihGKEYoNiMiIiE=

u(t-a)*f(t-a);

NiMqJi0lKkhlYXZpc2lkZUc2IywmJSJ0RyIiIiIiIyEiIkYpRidGKQ==

plot(%,t=0..5,scaling=constrained);

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

# Example 5I^2;

NiMhIiI=

Redefine I:interface(imaginaryunit=j);

NiNeIyIiIg==

# Check:j^2;

NiMhIiI=

I^2;

NiMqJCklIklHIiIjIiIi

de := diff(I(t),t,t) + 4*diff(I(t),t) = g;

NiM+JSNkZUcvLCYtJSVkaWZmRzYkLSUiSUc2IyUidEctJSIkRzYkRi0iIiMiIiIqJiIiJUYyLUYoNiRGKkYtRjJGMiUiZ0c=

G := 1/s - 2/s*exp(-s) + exp(-2*s)/s;

NiM+JSJHRywoKiYiIiJGJyUic0chIiJGJyooIiIjRidGKEYpLSUkZXhwRzYjLCRGKEYpRidGKSomLUYtNiMsJComRitGJ0YoRidGKUYnRihGKUYn

alias(J = laplace(I(t),t,s));

NiMlIkpH

eq := laplace(lhs(de),t,s) = G;

NiM+JSNlcUcvLCwqJiklInNHIiIjIiIiJSJKR0YrRistLSUiREc2IyUiSUc2IyIiISEiIiomRilGKy1GMUYyRitGNCooIiIlRitGKUYrRixGK0YrKiZGOEYrRjZGK0Y0LCgqJkYrRitGKUY0RisqKEYqRitGKUY0LSUkZXhwRzYjLCRGKUY0RitGNComLUY+NiMsJComRipGK0YpRitGNEYrRilGNEYr

subs({I(0)=0,D(I)(0)=0},%);

NiMvLCYqJiklInNHIiIjIiIiJSJKR0YpRikqKCIiJUYpRidGKUYqRilGKSwoKiZGKUYpRichIiJGKSooRihGKUYnRi8tJSRleHBHNiMsJEYnRi9GKUYvKiYtRjI2IywkKiZGKEYpRidGKUYvRilGJ0YvRik=

solve(%,J);

NiMsJCooLCgiIiIhIiIqJiIiI0YmLSUkZXhwRzYjLCQlInNHRidGJkYmLUYrNiMsJComRilGJkYuRiZGJ0YnRiZGLiEiIywmRi5GJiIiJUYmRidGJw==

Jsol := %;

NiM+JSVKc29sRywkKigsKCIiIiEiIiomIiIjRigtJSRleHBHNiMsJCUic0dGKUYoRigtRi02IywkKiZGK0YoRjBGKEYpRilGKEYwISIjLCZGMEYoIiIlRihGKUYp

F := 1/(s*(s^2+4));

NiM+JSJGRyomIiIiRiYqJiUic0dGJiwmKiQpRigiIiNGJkYmIiIlRiZGJiEiIg==

convert(F,parfrac,s);

NiMsJiooIiIlISIiJSJzRyIiIiwmKiQpRiciIiNGKEYoRiVGKEYmRiYqJkYoRigqJkYlRihGJ0YoRiZGKA==

invlaplace(F,s,t);

NiMsJiMiIiIiIiVGJSomI0YlRiZGJS0lJGNvc0c2IywkKiYiIiNGJSUidEdGJUYlRiUhIiI=

f := t -> 1/4 - 1/4*cos(2*t);

NiM+JSJmR2orNiMlInRHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0dGKCwmIyIiIiIiJUYuKiYjRi5GL0YuLSUkY29zRzYjLCQqJiIiI0YuOSRGLkYuRi4hIiJGKEYoRig2IyIiIQ==

Isol := f(t) - 2*f(t-1)*u(t-1) + f(t-2)*u(t-2);

NiM+JSVJc29sRywqIyIiIiIiJUYnKiYjRidGKEYnLSUkY29zRzYjLCQqJiIiI0YnJSJ0R0YnRidGJyEiIiooRjBGJywmRiZGJyomI0YnRihGJy1GLDYjLCYqJkYwRidGMUYnRidGMEYyRidGMkYnLSUqSGVhdmlzaWRlRzYjLCZGMUYnRidGMkYnRjIqJiwmRiZGJyomI0YnRihGJy1GLDYjLCYqJkYwRidGMUYnRidGKEYyRidGMkYnLUY8NiMsJkYxRidGMEYyRidGJw==

plot(Isol,t=0..5,-1..1);

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

# Alternate solution using dsolve:I := 'I';

NiM+JSJJR0Yk

de;

NiMvLCYtJSVkaWZmRzYkLSUiSUc2IyUidEctJSIkRzYkRisiIiMiIiIqJiIiJUYwLUYmNiRGKEYrRjBGMCUiZ0c=

g := 1*(u(t)-u(t-1)) -1*(u(t-1)-u(t-2)) + 0*u(t-2);

NiM+JSJnRywoLSUqSGVhdmlzaWRlRzYjJSJ0RyIiIiomIiIjRiotRic2IywmRilGKkYqISIiRipGMC1GJzYjLCZGKUYqRixGMEYq

de;

NiMvLCYtJSVkaWZmRzYkLSUiSUc2IyUidEctJSIkRzYkRisiIiMiIiIqJiIiJUYwLUYmNiRGKEYrRjBGMCwoLSUqSGVhdmlzaWRlR0YqRjAqJkYvRjAtRjc2IywmRitGMEYwISIiRjBGPC1GNzYjLCZGK0YwRi9GPEYw

dsolve({de,I(0)=0,D(I)(0)=0});

NiMvLSUiSUc2IyUidEcsNComIyIiIiIiJUYrKiYtJSpIZWF2aXNpZGVHNiMsJkYnRisiIiMhIiJGK0YnRitGK0YrKiYjIiIqIiM7RitGLkYrRjMqJiNGK0Y3RisqJkYuRistJSRleHBHNiMsJiomRixGK0YnRitGMyIiKUYrRitGK0YrKiZGKkYrKiYtRi9GJkYrRidGK0YrRisqJkY5RisqJi1GPDYjLCQqJkYsRitGJ0YrRjNGK0ZDRitGK0YrKiYjRitGN0YrRkNGK0YzKiYjRitGMkYrKiYtRi82IywmRidGK0YrRjNGK0YnRitGK0YzKiYjIiImRkBGK0ZPRitGKyomI0YrRkBGKyomRk9GKy1GPDYjLCYqJkYsRitGJ0YrRjNGLEYrRitGK0Yz

Isol2 := rhs(%);

NiM+JSZJc29sMkcsNComIyIiIiIiJUYoKiYtJSpIZWF2aXNpZGVHNiMsJiUidEdGKCIiIyEiIkYoRi9GKEYoRigqJiMiIioiIztGKEYrRihGMSomI0YoRjVGKComRitGKC0lJGV4cEc2IywmKiZGKUYoRi9GKEYxIiIpRihGKEYoRigqJkYnRigqJi1GLDYjRi9GKEYvRihGKEYoKiZGN0YoKiYtRjo2IywkKiZGKUYoRi9GKEYxRihGQUYoRihGKComI0YoRjVGKEZBRihGMSomI0YoRjBGKComLUYsNiMsJkYvRihGKEYxRihGL0YoRihGMSomIyIiJkY+RihGTkYoRigqJiNGKEY+RigqJkZORigtRjo2IywmKiZGKUYoRi9GKEYxRilGKEYoRihGMQ==

plot(Isol2,t=0..5,-1..1);

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

# Remark: dsolve has clearly made an error in finding this solution.# Example 6 Sum(t^(2*n+1)*(-1)^n/(2*n+1)!,n=0..3);

NiMtJSRTdW1HNiQqKCklInRHLCYqJiIiIyIiIiUibkdGLEYsRixGLEYsKSEiIkYtRiwtJSpmYWN0b3JpYWxHNiNGKUYvL0YtOyIiISIiJA==

value(%);

NiMsKiUidEciIiIqJiNGJSIiJ0YlKiQpRiQiIiRGJUYlISIiKiYjRiUiJD8iRiUqJClGJCIiJkYlRiVGJSomI0YlIiVTXUYlKiQpRiQiIihGJUYlRiw=

f7 := %/t;

NiM+JSNmN0cqJiwqJSJ0RyIiIiomI0YoIiInRigqJClGJyIiJEYoRighIiIqJiNGKCIkPyJGKCokKUYnIiImRihGKEYoKiYjRigiJVNdRigqJClGJyIiKEYoRihGL0YoRidGLw==

f7 := simplify(%);

NiM+JSNmN0csKiIiIkYmKiYjRiYiIidGJiokKSUidEciIiNGJkYmISIiKiYjRiYiJD8iRiYqJClGLCIiJUYmRiZGJiomI0YmIiVTXUYmKiQpRixGKUYmRiZGLg==

laplace(f7,t,s);

NiMsKiomIiIiRiUlInNHISIiRiUqJkYlRiUqJiIiJEYlKUYmRipGJUYnRicqJkYlRiUqJiIiJkYlKUYmRi5GJUYnRiUqJkYlRiUqJiIiKEYlKUYmRjJGJUYnRic=

taylor(arctan(x),x,8);

NiMrLSUieEciIiJGJSMhIiIiIiRGKCNGJSIiJkYqI0YnIiIoRiwtJSJPRzYjRiUiIik=

subs(x=1/s,%);

NiMsLComIiIiRiUlInNHISIiRiUqJkYlRiUqJiIiJEYlKUYmRipGJUYnRicqJkYlRiUqJiIiJkYlKUYmRi5GJUYnRiUqJkYlRiUqJiIiKEYlKUYmRjJGJUYnRictJSJPRzYjKiZGJUYlKiQpRiYiIilGJUYnRiU=