How to quickly "plug in" numerical values into symbolic equations to get a numerical result

Setup:

syms s

fs = (-2*(s-1))/((s+1)*(s+2));

fs1 = (1/s)*fs;

yt1 = ilaplace(fs1)

At this point Matlab returns the following symbolic equation:

yt1 = 3*exp(-2*t) - 4*exp(-t) + 1

To find yt1 when t = 0 and t = inf I can do the following:

yt1_0 = 3*exp(-2*0) - 4*exp(-0) + 1

yt1_inf = 3*exp(-2*inf) - 4*exp(-inf) + 1

But I was hoping that there is a smarter way to manipulate symbolic equations like:

yt1(t ==0)

yt1(t ==inf)

Or something like that so I do not have to write out the entire equation and update "t" as I have above.

Thoughts?

Thank you,

C

Answer 1

[Voss]

You can use subs() to do that. It will evaluate yt1 and give you a symbolic value, on which you can use double() to convert to a numeric value.

syms s
fs                      = (-2*(s-1))/((s+1)*(s+2));
fs1                     = (1/s)*fs;
yt1 = ilaplace(fs1)

yt1 = 

t = 0;
yt1_0 = subs(yt1);

t = Inf;
yt1_inf = subs(yt1);

display(yt1_0); display(yt1_inf);

yt1_0 = 

0

yt1_inf = 

1

yt1_0 = double(yt1_0);
yt1_inf = double(yt1_inf);

display(yt1_0); display(yt1_inf);

yt1_0 = 0

yt1_inf = 1

[Voss]

Better yet, do both values of t at once:

syms s
fs                      = (-2*(s-1))/((s+1)*(s+2));
fs1                     = (1/s)*fs;
yt1 = ilaplace(fs1)

yt1 = 

t = [0 Inf];
yt1_0_inf = subs(yt1);
display(yt1_0_inf);

yt1_0_inf = 

yt1_0_inf = double(yt1_0_inf);
display(yt1_0_inf);

yt1_0_inf = 1×2

0 1