%% L02_Laplace
%% ==============
%% Function to find laplace-transform using Matlab symbolic toolbox.
%%
%% Created  : 15 July 2005
%% Modified : 15 July 2005
%%
%% Copyright (c) 2005 Salman Durrani .
%% ------------------------------------------------------------

%% clear matlab memory 
clear all;
clc

syms f b w t s

%% Take Laplace Transform

%% Example 1: Unit step u[n]
f = heaviside(t);
Ans1=maple('laplace',f,t,s)

%% Example 2:
f = (t^4);
Ans2=maple('laplace',f,t,s)

%% Example 3:
f= t*sin(w*t);
Ans3=maple('laplace',f,t,s)
pretty(Ans3)

%% Example 4:
f= exp(t)*cos(w*t);
Ans4=maple('laplace',f,t,s)
pretty(Ans4)

%% Take Inverse Laplace Transform

%% Example 1: 
F = 1/(s^2+s);
Ans1=maple('invlaplace',F,s,t)
pretty(Ans1)

%% Example 2: 
F = s/((s^2+b^2))^2;
Ans2=maple('invlaplace',F,s,t)
pretty(Ans2)

%% Example 3: 
F = (3*s)/(s^2+2*s-8);
Ans3=maple('invlaplace',F,s,t)
pretty(Ans3)