Lectures related to Fourier Series: Properties and Examples

Fourier Series and Equations

Covers Fourier series, periodic functions, and Fourier transforms.

Probability and Statistics

Covers mathematical concepts from number theory to probability and statistics.

Fourier Coefficients: Trigonometric Series

Explores Fourier coefficients in trigonometric series, emphasizing even and odd functions.

Continuous Functions: Integrability and Examples

Explores continuous functions and integrability through practical examples.

Fourier Series: Examples

Explores examples of Fourier series coefficients and applications in various functions.

Transformations and Inversions: Laplace and Fourier

Discusses Laplace and Fourier transformations, focusing on their inversion formulas and applications in solving differential equations.

Fourier Series: Convergence and Dirichlet Theorem

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

Discrete Fourier Transform: Lecture 12

Explores the Discrete Fourier Transform, Fast Fourier Transform, orthogonal functions, and trigonometric approximations.

Distribution & Interpolation Spaces

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Functions Composition: Continuity & Elements

Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.

Fourier Series: Periodic Functions and Calculations

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

Properties of Fourier Transform: Continuity, Linearity, Derivative

Explores the properties of Fourier transformations, including continuity, linearity, and derivatives.

Integral Techniques: Integration by Parts

Explores the integration by parts technique through examples, showcasing its step-by-step application to functions like cos(x) and sin(x.

Harmonic Analysis: Classical Theory and Fourier Series

Covers classical harmonic analysis on the circle, Fourier series convergence, and applications in PDEs.

Fourier Transform: L^2 Analysis

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

Fourier Series: Extension and Periodicity

Covers the extension and periodicity of Fourier series and the interpretation of coefficients.

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: Applications and Examples

Explores the application of Fourier series and the challenges of using multiple methods to solve problems.

Neurophysiological Data Analysis

Explores neurophysiological data analysis, covering AP identification, firing rates, subthreshold activity, FFT spectral analysis, and event-triggered analysis using MATLAB.

Topologie: Exercice 4

Covers Exercise 4 in Topology, focusing on continuous functions and constructing functions.