Lectures related to Fourier Series: Understanding Signals and Transformations

Improper Integrals: Convergence and Comparison

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.

Complex Integration: Fourier Transform Techniques

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

Fourier Series: Periodic Functions and Calculations

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

Convergence of Fourier Series

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

Comparison Series and Integrals

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

Improper integrals: Techniques and Examples

Covers examples of integration by substitution and rational functions.

Generalized Integrals: Type 2

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

Improper Integrals: Fundamental Concepts and Examples

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

Integration Techniques: Change of Variable and Integration by Parts

Explores advanced integration techniques such as change of variable and integration by parts to simplify complex integrals and solve challenging integration problems.

Generalized Integrals: Convergence and Divergence

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.

Fourier Transform: L^2 Analysis

Explores the Fourier transformation on L^2, emphasizing convergence and density in Fourier analysis.

Analysis I Exam Solutions

Provides solutions to an Analysis I exam, covering various topics.

Advanced Analysis II: Integrals and Functions

Covers advanced topics in analysis, focusing on integrals, functions, and their properties.

Geometric Examples: Triangles and Functions

Explores geometric examples of triangles and functions, demonstrating the variation of x and y within defined ranges.

Fourier Series: Periodic Functions and Sine/Cosine Interactions

Covers the Fourier series and interactions between sine and cosine functions.

Fourier Series: Convergence and Dirichlet Theorem

Covers Fourier series convergence, Dirichlet theorem, and applications in signal processing.

Uniform Convergence of Fourier Series

Covers the concept of uniform convergence of Fourier series and Dirichlet's theorem application.

Fourier Coefficients of Periodic Functions

Explores computing Fourier coefficients of periodic functions, discussing convergence and reconstruction of the original signal.