Laplace Transforms


% 1. Constant Function
syms t s;
f1 = 1;
F1= laplace(f1, t, s);
pretty(F1)

% 2. Exponential Decay
syms t a s;
f2 = exp(-a*t);
F2 = laplace(f2, t, s);
pretty(F2)

% 3. Unit Step Function
syms t s;
f3 = heaviside(t);
F3= laplace(f3, t, s);
pretty(F3)

% 4. Impulse Function
syms t s;
f4= dirac(t);
F4 = laplace(f4, t, s);
pretty(F4)


% 5. Sinusoidal Function
syms t omega s;
f5 = sin(omega*t);
F5 = laplace(f5, t, s);
pretty(F5)

% 6. Cosinusoidal Function
syms t omega s;
f6 = cos(omega*t);
F6 = laplace(f6, t, s);
pretty(F6)

% 7. Exponential Growth
syms t a s;
f7 = exp(a*t);
F7 = laplace(f7, t, s);
pretty(F7)

% 8. Ramp Function
syms t s;
f8 = t;
F8 = laplace(f8, t, s);
pretty(F8)

% 9. Heaviside Function Shifted
syms t a s;
f9 = heaviside(t - a);
F9 = laplace(f9, t, s);
pretty(F9)


% 10. Polynomial Function
syms t s n;
f10 = t^n;
F10 = laplace(f10, t, s);
pretty(F10)

-------------------------------------------------------------
Inverse Laplace Transforms
syms t s a omega n;

% 1. Inverse Laplace of 1/s
syms t s;
F1 = 1/s;
f1= ilaplace(F1, s, t);
pretty(f1)

% 2. Inverse Laplace of 1/(s + a)
syms t s a;
F2 = 1/(s + a);
f2 = ilaplace(F2, s, t);
pretty(f2)

% 3. Inverse Laplace of 1/s^2
syms t s;
F3 = 1/s^2;
f3 = ilaplace(F3, s, t);
pretty(f3)

% 4. Inverse Laplace of 1
syms t s;
F4 = 1;
f4 = ilaplace(F4, s, t);
pretty(f4)


% 5. Inverse Laplace of omega/(s^2 + omega^2)
syms t s omega;
F5 = omega/(s^2 + omega^2);
f5 = ilaplace(F5, s, t);
pretty(f5)

% 6. Inverse Laplace of s/(s^2 + omega^2)
syms t s omega;
F6 = s/(s^2 + omega^2);
f6 = ilaplace(F6, s, t);
pretty(f6)

% 7. Inverse Laplace of 1/(s - a)
syms t s a;
F7 = 1/(s - a);
f7 = ilaplace(F7, s, t);
pretty(f7)

% 8. Inverse Laplace of e^(-as)/s
syms t s a;
F8 = exp(-a*s)/s;
f8 = ilaplace(F8, s, t);
pretty(f8)

% 9. Inverse Laplace of 1/(s^2 + a^2)^2
syms t s a;
F9 = 1/((s^2 + a^2)^2);
f9= ilaplace(F9, s, t);
pretty(f9)

% 10. Inverse Laplace of e^(as)
syms t s a;
F10 = exp(a*s);
f10 = ilaplace(F10, s, t);
pretty(f10)