Lectures related to Self Similar Solutions and Stokes Second Problem

Fourier and Laplace Transforms: Concepts and Applications

Provides an overview of Fourier and Laplace transforms, their properties, and applications in signal analysis.

Fourier Transform: Derivatives and Formulas

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

Poisson Problem: Fourier Transform Approach

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.

Fourier Transform: Derivatives and Laplace Transform

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

Stokes first problem: hydrodynamic separation of variables

Explores the application of separation of variables in hydrodynamics and the concept of self-similarity.

Frequency Response of LTI Systems

Explores LTI systems, impulse response, convolution, system properties, and frequency response, including low-pass and band-pass filters.

Signals, Instruments, and Systems: System Properties and Transforms

Introduces system properties, Laplace Transform, and analog filters for signal analysis.

Laplace Transform: Basics and Properties

Covers the basics of the Laplace transform, properties, and applications to LTI systems, including transfer function and frequency response.

Harmonic Analysis: Schwerte Functions

Explores Schwerte functions in harmonic analysis, emphasizing compact support and function convergence.

Region of Convergence: Properties and Laplace Transform

Covers the concept of Region of Convergence (ROC) and Laplace transform properties.

Viscoelastic Materials: Models and Transformations

Explores viscoelastic materials, transforms, and models in materials science.

Fourier transforms: Light-matter interaction

Explores Fourier and Laplace transforms in materials science, focusing on light-matter interaction, diffraction patterns, and crystal properties.

Convolution and Laplace Transform

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

Partial Fraction Expansion

Introduces Partial Fraction Expansion as a valuable tool for analyzing stable LTI systems.

Laplace Transform: Basics

Introduces Laplace transform, ROC, and LTI systems with transfer functions and frequency response.

Laplace Transform and LTI Systems

Covers Laplace Transform, Fourier Transforms, transfer functions, LTI systems, and Region of Convergence properties.

Properties of Fourier and inverse Fourier transforms

Explores the properties of Fourier and inverse Fourier transforms, analyzing finite wave trains, Gaussian functions, and 3D space transformations.

Introduction to the Laplace Transform

Covers the Laplace Transform, LTI systems, Fourier Transforms, and properties.

Introduction to the z-Transform

Covers the z-Transform, LTI systems, and signal processing applications.

Probability and Statistics

Covers mathematical concepts from number theory to probability and statistics.