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All the Mathematics You Missed by Lori Pedersen, Thomas A. Garrity

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Chapter 13

Fourier Analysis

Basic Object:

Real-valued functions with a fixed period

Basic Maps:

Fourier transforms

Basic Goal:

Finding bases for vector spaces of periodic functions

13.1  Waves, Periodic Functions and Trigonometry

Waves occur throughout nature, from water pounding a beach to sound echoing off the walls at a club to the evolution of an electron’s state in quantum mechanics. For these reasons, at the least, the mathematics of waves is important. In actual fact, the mathematical tools developed for waves, namely Fourier series (or ...

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