Lectures related to Distributions and Laplace Transform: Key Concepts

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

Signals & Systems I: Distributions and Linear Systems

Covers distributions, linear systems, impulse response, convolution, and examples of linear systems.

Fourier Transform: Concepts and Applications

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

Differential Calculus: Applications and Reminders

Covers differential calculus applications and reminders, emphasizing the importance of differentiability in mathematical analysis.

Distributions & Interpolation Spaces

Covers distributions, interpolation spaces, convergence, and the concept of dual spaces.

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Fundamental Solutions of Laplace Equation

Explores fundamental solutions, Green's formula, distributions, and convergence in Laplace equation.

Dirac Delta Function and ODEs

Covers the Dirac delta function, Laplace transforms, and unimolecular reactions with convolution emphasis.

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Fourier Transform: Derivatives and Formulas

Explores Fourier transform properties with derivatives, crucial for solving equations, and introduces the Laplace transform for signal transformation.

Semi-groups of Contractions

Explores semi-groups of contractions, discussing uniqueness theorems, maximum principles, and the infinitesimal generator.

Transformations and Inversions: Laplace and Fourier

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

Laplace Transform: Properties and Applications

Covers the properties and applications of the Laplace transform in solving differential equations.

Differential Equations: Solutions and Functions

Explores solutions of differential equations and properties of functions.

Canonical Transformations: Hamilton-Jacobi Equation

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

Convolution and Laplace Transform

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

Partial Derivatives and Differential Equations

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

Exact Linearization: Determining Conditions and Transformations

Explores exact linearization, determining conditions and transformations using Lie bracket and hook of Lie.

Linear Homogeneous Equations

Covers second-order linear homogeneous differential equations and their solutions.

Laplace Transform: Solving Differential Equations

Discusses the application of the Laplace transform to solve differential equations and explores its properties and examples.