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Worked example showing the application of the separated solution and the d'Alembert methods to the 1D wave equation

Worked example showing the calculation of the Fourier series of a periodic function

Solution of a system of differential equations with the Laplace transform method.

Worked solution for Question 1 from Exercise sheet ODE 1 from EM2A

Video discussing the complex Fourier series

Video discussing the harmonic oscillator. We use the Fourier series of a periodic forcing to find the particular solution of the differential equation describing the harmonic oscillator.

Three examples showing the use of differentiation and integration to find Fourier series.

Video showing how to solve differential equations with periodic forcing functions with the Fourier series.

Video showing how to use differentiation and integration to find the Fourier series of a function from known Fourier series.

This video shows how we can use shape preserving transforms to calculate the Fourier series of the square pulse from the Fourier series of the square wave.

This example uses shape preserving transforms to calculate the Fourier series of a sawtooth function from the Fourier series of a sawtooth function with a different period.

Example calculating the full-range extension for the non-periodic square function.

Example showing the calculation of the Fourier series of the sawtooth function.

This video introduces shape preserving transformations and how these can be used to find the Fourier series from similar functions.

This video discusses the half-range odd extension of non-periodic functions.

Video introducing the half-range even extension for non-periodic functions.