Lectures related to Fourier Series: Theory and Applications

Fourier Series: Understanding Coefficients and Periodicity

Explores Fourier series coefficients, periodicity, and series relations.

Fourier Series: Periodic Functions and Sine/Cosine Interactions

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

Determinantal Point Processes and Extrapolation

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Uniform Convergence of Fourier Series

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

Laplace Transform: Basics

Covers the Laplace transform, region of convergence, impulse response, and multiple poles.

Fourier Transform: Analysis IV

Covers the Fourier transform in Analysis IV, discussing Fourier series and solutions for various problems.

Fourier Series: Dirichlet Theorem and Convergence

Explores Fourier series, Dirichlet theorem, and convergence properties in periodic functions.

Fourier Series: Periodic Functions

Explores Fourier series for periodic functions, emphasizing coefficient calculation and function representation using sine and cosine terms.

Z-Transform: Convergence and Poles

Covers the Z-transform, region of convergence, and examples of signals with multiple poles and finite-duration signals.

Integration: Lecture 8

Covers the integration of functions and Fourier series with examples and exercises.

Fourier Series: Convergence and Dirichlet Theorem

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

Fourier Series: Convergence and Coefficients

Explores Fourier series convergence and coefficient calculations through examples and derivations.

Vibration of Diatomic Molecules

Explores the vibration of diatomic AB molecules and Fourier series, emphasizing equations of motion and Dirichlet's theorem.

Vector Representation of Signals

Explores the vector representation of signals, orthogonal functions, and Fourier series.

Fourier Series: Properties and Calculations

Explores Fourier series properties, calculations, convergence, and coefficient significance.

Fourier Series: Odd and Even Functions

Explores odd and even functions in Fourier series applications, including half-range series and cosine/sine series.

Fourier Series Interpretation

Explores the interpretation of Fourier series from basic to complex signals, demonstrating the concept through animations and explaining the relationship between sine waves and circles.

Pointwise Convergence of Fourier Series

Explores the pointwise convergence of Fourier series and its applications in optimal transport.

Fourier Series: Approximation and Transformations

Covers the concept of Fourier series and their practical applications in signal processing.

Convergence of Fourier Series

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