Fourier Series: Understanding Signals and Transformations

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Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Explores integration techniques, including indefinite integrals and variable changes, through trigonometric functions.

Explores the intuition behind transforms of the place and addresses audience questions on integral calculations and function choices.

Discusses complex integration techniques for calculating Fourier transforms and introduces the Laplace transform's applications.

Covers Fourier series for periodic functions and calculations involving Fourier coefficients.

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.

Explores the relationship between series and integrals, highlighting convergence criteria and function examples.

Covers examples of integration by substitution and rational functions.

Covers the integration of limit expansions and continuous functions by pieces.

Covers improper integrals, their definitions, properties, and examples in two and three dimensions.