Lectures related to Convolution and Fourier Transform

Bounded Operators: Theory and Applications

Covers bounded operators between normed vector spaces, emphasizing the importance of continuity and exploring applications like the Fourier transform.

Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.

Functional Analysis and Distribution Theory

Explores different notions of function equality, linear functionals, operations on distributions, and the advantages of working with Schwartz' space.

Dispersion and Schrödinger Equation Solution

Explores the solution of the 1D Schrödinger equation using Fourier transforms and convolution techniques.

Convolution and Laplace Transform

Explores control of dynamic systems, impulse response, Laplace transform, and Fourier transform for solving differential equations.

Dynamical Approaches to Spectral Theory of Operators

Explores dynamical approaches to the spectral theory of operators, focusing on self-adjoint operators and Schrödinger operators with dynamically defined potentials.

MHD Stability and Equilibrium

Explores MHD equilibrium and stability, emphasizing energy considerations for determining stability.

Postulates of Quantum Mechanics

Explains the postulates of Quantum Mechanics, focusing on self-adjoint operators and mathematical notation.

Fourier Analysis: Fourier Series and Transform

Explores Fourier series, DFT, FFT, and their applications in signal processing and spectroscopy.

Distributions and Derivatives Log in to Mediaspace to watch this video

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Distributional Derivatives Log in to Mediaspace to watch this video

Explores distributional derivatives, continuity, boundedness of linear operators, and weak-* continuity.

Heat and Wave Equations: Analysis IV Log in to Mediaspace to watch this video

Covers the study of the heat and wave equations, including the process of separating variables to find solutions.

Extension of Linear Transformations Log in to Mediaspace to watch this video

Covers the extension of bounded linear transformations and the free propagator in L^2 spaces.

Equations of Heat and Fourier Transform Log in to Mediaspace to watch this video

Covers heat equations, Fourier transforms, and variable separation methods.

Free Propagation and Heat Equation Log in to Mediaspace to watch this video

Covers free propagation and the heat equation solution, discussing momentum preservation and Fourier multipliers.

Dual Spaces: Definitions and Properties Log in to Mediaspace to watch this video

Covers the definitions and properties of dual spaces and linear operators.

Fourier Transform and Partial Differential Equations Log in to Mediaspace to watch this video

Explores the application of Fourier transform to PDEs and boundary conditions.

Complex Analysis: Residue Theorem and Fourier Transforms Log in to Mediaspace to watch this video

Discusses complex analysis, focusing on the residue theorem and Fourier transforms, with practical exercises and applications in solving differential equations.

Quantum Mechanics: Mathematical Framework Log in to Mediaspace to watch this video

Introduces the need for a mathematical framework to describe linear operators on infinite-dimensional Hilbert spaces in quantum mechanics.

Fourier Transform: Concepts and Applications Log in to Mediaspace to watch this video

Covers the Fourier transform, its properties, applications in signal processing, and differential equations, emphasizing the concept of derivatives becoming multiplications in the frequency domain.