 # Laplace Transform: First Shifting Theorem

A series of free Engineering Mathematics Lessons.

Introduction to Laplace transform
Motivation
Laplace transforms find uses in solving initial value problems that involve linear, ordinary differential equations with constant coefficients. These types of problems usually arise in modelling of phenomena. Laplace transforms offer an advantage over other solution methods to initial value problems as they streamline the process and can easily deal with discontinuous forcing functions.

This is a basic introduction to the Laplace transform and how to calculate it. Such ideas are seen in university mathematics.
Laplace transform + differential equations
This video shows how to solve differential equations by the method of Laplace transforms. Such ideas are seen in university mathematics.

First shifting theorem of Laplace transforms
The first shifting theorem provides a convenient way of calculating the Laplace transform of functions that are of the form
f(t) := e-atg(t)
where a is a constant and g is a given function.

This video shows how to apply the first shifting theorem of Laplace transforms. Several examples are presented to illustrate how to take the Laplace transform and inverse Laplace transform and are seen in university mathematics.
Laplace Transform: First Shifting Theorem
Here we calculate the Laplace transform of a particular function via the "first shifting theorem". This video may be thought of as a basic example. The first shifting theorem is a useful tool when faced with the challenge of taking the Laplace transform of the product of exponential function with another function. The Laplace transform is very useful in solving ordinary differential equations.

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