JSFH
restart: with(plots):
plot(Heaviside(x),x=-5..5);
alias(u=Heaviside):
plot( u( x+2 ));
plot( u( -x));
plot( u( x-4 ));
plot( u( 2*x ));
plot( u( 2*x + 1 ));
plot( u( 3-x ));
p1:=plot(x^2):
p2:=plot(x^2 * u(x-2)):
p3:=plot(x^2 * u(2-x)):
display(array([p1,p2,p3]));
f:=x->x^2;
p1:=plot(f(x-2),x=-5..5):
p2:=plot(f(x-2) * u(x),x=-5..5):
p3:=plot(f(x-2) * u(x-2),x=-5..5):
display(array([p1,p2,p3]));
p1:=plot(2*x+1, x=-5..5):
p2:=plot((2*x+1) * u(x+2), x=-5..5):
p3:=plot((2*x+1) * u(2-x), x=-5..5):
p4:=plot(2(x-2)+1 * u(x-2), x=-5..5):
display(array([p1,p2,p3,p4]));
plot(u(x+2)-u(x-2),x=-5..5);
plot( (x+4) * (u(x+4) - u(x+2)) + 2*(u(x+2)-u(x-2)) + (4-x) * (u(x-2) - u(x-4)), x=-5..5);
plot(exp(-2*x) * u(x));
plot( u(x+2) - u(x-2));
f:=x-> sqrt(N/Pi)*exp(-N*x^2);
plot( u(x+2) - u(x) +2*u(x) - 2*u(x-4));
plot( x^2*(u(x+1) - u(x-1)), x=-2..2 );
integrate(f(x),x=-infinity..infinity);
integrate(exp(-x^2)*u(x), x=0..infinity);
integrate(exp(-x^2)*u(x-2), x=-infinity..infinity);
plot([subs(N=5,f(x)),subs(N=10,f(x)),subs(N=20,f(x))],x=-2..2);
g:=x->1/a * ( ((1+x/a)*(u(x+a) - u(x)) + (1-x/a)*(u(x) - u(x-a))) );
plot([subs(a=5,g(x)),subs(a=3,g(x)),subs(a=1,g(x))]);
integrate((5*x-3)*Dirac(x+1),x=0..7);
Integrate((5*x-3)*Dirac(x+1),x=0..7) = integrate((5*x-3)*Dirac(x+1),x=0..7);
integrate(cos(tan(exp(x)))*Dirac(x-1), x=-infinity..infinity);
<1,3>;
<<1,3>|<2,4>>;
<<4,-2,0>|<-2,4,-2>|<0,-2,4>>;
<<4|-2|0>,<-2|4|-2>,<0|-2|4>>;
c1:=<4,-2,0>;
c2:=<-2,4,-2>;
c3:=<0,-2,4>;
r1:=<4|-2|0>;
r2:=<-2|4|-2>;
r3:=<0|-2|4>;
<c1|c2|c3>;
<r1,r2,r3>;
with(LinearAlgebra):
Matrix([[2,4],[6,8]]);
IdentityMatrix(7);
Matrix(4,3,[-1,0,1,-2,0,2,-3,0,3,-4,0,4]);
Matrix(4,4,(i,j)->1/(i+j-1));
HilbertMatrix(10);
VandermondeMatrix(<1,2,3,4>);
TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMzUyNDUyNDcwWColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiIyIjIiIiIiIkRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMzUwNzQwNzE4WCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjJSIjIiMiIiIiIiQiIiMiIiVGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMzUwNzQxMTk4WCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjKiIkIiQiIiUhIiMiIiFGJ0YmRidGKEYnRiZGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMzUwNzQxNjc4WCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjKiIkIiQiIiUhIiMiIiFGJ0YmRidGKEYnRiZGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMzUwNzQyMzk4WColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiJCIkIiIlISIjIiIhRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMzUwNzQyNjM4WColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiJCIkISIjIiIlRiZGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMzUwNzQyNzU4WColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiJCIkIiIhISIjIiIlRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMzUwNzQyODc4WColKWFueXRoaW5nRzYiRiVbZ2whJCUhISEiJCIkIiIlISIjIiIhRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMzUwNzQyOTk4WColKWFueXRoaW5nRzYiRiVbZ2whJCUhISEiJCIkISIjIiIlRiZGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMzUwNzQzMTE4WColKWFueXRoaW5nRzYiRiVbZ2whJCUhISEiJCIkIiIhISIjIiIlRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMzUwNzQzNTk4WCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjKiIkIiQiIiUhIiMiIiFGJ0YmRidGKEYnRiZGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMjQ2NDUyNDYyWCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjKiIkIiQiIiUhIiMiIiFGJ0YmRidGKEYnRiZGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMjQ2NDUyOTQyWCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjJSIjIiMiIiMiIiciIiUiIilGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMjQ2NDU0MjYyWCwlKWFueXRoaW5nRzYjJSlpZGVudGl0eUc2IltnbCEiIiEhISMhIigiKEYnTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMjQ2NDU1NzAyWCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjLSIlIiQhIiIhIiMhIiQhIiUiIiFGKkYqRioiIiIiIiMiIiQiIiVGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMjQ2NDQ5MDg2WCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjMSIlIiUiIiIjRiYiIiMjRiYiIiQjRiYiIiVGJ0YpRisjRiYiIiZGKUYrRi0jRiYiIidGK0YtRi8jRiYiIihGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMjQ2NDQ5OTI2WCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjX3EiKyIrIiIiI0YmIiIjI0YmIiIkI0YmIiIlI0YmIiImI0YmIiInI0YmIiIoI0YmIiIpI0YmIiIqI0YmIiM1RidGKUYrRi1GL0YxRjNGNUY3I0YmIiM2RilGK0YtRi9GMUYzRjVGN0Y5I0YmIiM3RitGLUYvRjFGM0Y1RjdGOUY7I0YmIiM4Ri1GL0YxRjNGNUY3RjlGO0Y9I0YmIiM5Ri9GMUYzRjVGN0Y5RjtGPUY/I0YmIiM6RjFGM0Y1RjdGOUY7Rj1GP0ZBI0YmIiM7RjNGNUY3RjlGO0Y9Rj9GQUZDI0YmIiM8RjVGN0Y5RjtGPUY/RkFGQ0ZFI0YmIiM9RjdGOUY7Rj1GP0ZBRkNGRUZHI0YmIiM+RiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDgwMjQ2NDUxMTI2WCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjMSIlIiUiIiJGJkYmRiZGJiIiIyIiJCIiJUYmRikiIioiIztGJiIiKSIjRiIja0Yl