Lectures related to Fourier Series: Dirichlet Theorem and Convergence

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.

Fourier Series: Understanding Periodicity and Coefficients

Explores t-periodic functions in Fourier series, discussing intervals, propositions, and variable changes for coefficient calculation and series convergence.

Fourier Series: Approximation and Convergence

Introduces Fourier series, explaining their approximation properties and convergence, along with the Dirichlet theorem and coefficient computation.

Vibration of Diatomic Molecules

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

Uniform Convergence of Fourier Series

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

Generalized Integrals: Type 2

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

Pointwise Convergence of Fourier Series

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

Fourier Series: Understanding Signals and Transformations

Explores Fourier series, left and right limits, theorem proofs, and exam formats.

Convergence of Fourier Series

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

Fourier Series: Properties and Calculations

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

Fourier Series: Theory and Applications

Explores the theory and applications of Fourier series, including convergence properties and piecewise-defined functions.

Signals & Systems I: Fourier Transform and Dirac Pulse

Explores Fourier transformation, sign function, Dirac pulse, series development, and periodic signal synthesis.

Limit of Functions: Convergence and Boundedness

Explores limits, convergence, and boundedness of functions and sequences.

Lebesgue Measure and Fourier Analysis

Explores Lebesgue measure, Fourier analysis, PDE applications, and optimal transport in PDEs.

Dirichlet Series

Explores Dirichlet series convergence properties and absolute convergence conditions, with examples and applications.

Fourier Series: Theory and Comparison

Delves into Fourier series theory, computation, and comparison with functions using the Dirichlet theorem.

Unbounded and Bounded Systems: Fourier Methods

Explores the spectral properties of unbounded and bounded systems using Fourier methods and emphasizes the importance of choosing the correct representation for different boundary conditions.

Taylor Series: Convergence and Applications

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

Fourier Coefficients of Periodic Functions

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