May 2022
Intermediate to advanced
487 pages
9h 22m
English
Content preview from Differential Equations, 3rd Edition
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7Fourier Series: Basic Concepts
The idea of Fourier series
Calculating a Fourier series
Convergence of Fourier series
Odd and even functions
Fourier series on arbitrary intervals
Orthogonality
7.1 Fourier Coefficients
Trigonometric and Fourier series constitute one of the oldest parts of analysis. They arose, for instance, in classical studies of the heat and wave equations. Today they play a central role in the study of sound, heat conduction, electromagnetic waves, mechanical vibrations, signal processing, and image analysis and compression. Whereas power series (see Chapter 4) can only be used to represent very special functions (most functions, even smooth ones, do not have convergent power series), Fourier ...
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