Lectures related to Green's Function: Theory and Applications

Vibrating Strings: Mathematical Analysis and Fourier Series

Provides an overview of the mathematical analysis of vibrating strings using Fourier series and Laplace transforms.

Cauchy Problem: Differential Equations and Initial Conditions

Covers the Cauchy problem, focusing on differential equations and the role of initial conditions in determining unique solutions.

Advanced Analysis II: Differential Equations and Timers

Discusses advanced analysis concepts, focusing on differential equations and timers in microcontrollers.

Differential Equations and Heat Diffusion

Covers differential equations, heat diffusion, and advanced analysis for engineers.

Advanced Analysis II: Cauchy Problem and Differential Equations

Covers the Cauchy problem in differential equations, focusing on initial conditions and their impact on 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.

Fundamental Solutions of Laplace Equation

Covers the fundamental solutions of the Laplace equation and introduces distributions.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Advanced Analysis II: Cauchy Problem Resolution

Covers the resolution of a Cauchy problem using the method of variation of constants in differential equations.

Uniformly Elliptic Operators

Explores uniformly elliptic operators, their properties, and applications in solving differential equations and boundary value problems.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Poisson Problem: Fourier Transform Approach

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

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Quantum Mechanics: Power Series Solutions

Explores power series solutions in quantum mechanics for differential equations and energy quantization.

Homogeneous Solutions: Linear Independence

Explores finding particular solutions for homogeneous differential equations, emphasizing linear independence and variation of constants.

Differential Equations Solutions

Covers solutions of differential equations with initial conditions and boundedness concepts.

Material Point Model: Basics

Covers the material point model, initial conditions, and Newton's laws in physics.

Vibratory Mechanics: Continuous Systems

Explores vibratory mechanics in continuous systems, covering separation of variables, boundary conditions, and harmonic solutions.

Cauchy Problem: Initial Conditions

Discusses the Cauchy problem for ODEs with initial conditions and the importance of homeomorphism and Lipschitz continuity.

Laplace Transform: Solving Differential Equations

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