SimReal / Python / Matlab: Programming - Exercise - Mathematics - Laplace UiA Logo



SimReal - Python - Matlab 		001.

The function Heaviside Heaviside(t-a) in the library 'is often used in Laplace transformations.
This function in the symbolic Python library sympy is equal to zero for t less than a, else equal one (see figure).
Write a Python application that draw the graph of the Heaviside function that is equal to one for t greater or equal a =5.
Use the library sympy in Python for symbolic calculations.
Use sympy plot function for drawing graphs.
Use the Greek letter θ for the Heaviside function.

SimReal - Python - Matlab 		002.

We have the following function: f(t) = e-at.

Write an application that find the Laplace transformed and the inverse Laplace transformed of this function.
Print the expression of f, the Laplace transformed and the inverse Laplace transformed.
Draw the graph of the original function f and the inverse Laplace transformed of this function for a = 2.

Use the library sympy in Python for symbolic calculations.
Use sympy plot function for drawing graphs.

SimReal - Python - Matlab 		003.

Write an application that find the Laplace transformed of the following list of functions:

1, t, e-at, te-at, sinωt, cosωt, 1-e-at, e-atsinωt, e-atcosωt.

Use the library sympy in Python for symbolic calculations.
Use for Greek letters.

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