Lectures related to Energy Conservation in Wave Equations

Numerical Analysis: Stability in ODEs

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

Differential Equations: Speed Variation Analysis

Covers the analysis of speed variation using differential equations and small time intervals.

Canonical Transformations: Existence and Equations

Explores canonical transformations, focusing on existence, equations, simplicity, and differential equations' theory.

Differential Equations: Initial Conditions and Solutions

Covers the solution of differential equations with initial conditions and limit analysis.

One Dimensional Harmonic Oscillator

Explores the one-dimensional harmonic oscillator, equilibrium positions, and forced oscillators with external forces.

Material Point Model: Basics

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

Ordinary Differential Equations: Basics

Introduces the basics of ordinary differential equations, exploring existence, uniqueness, higher dimensions, Lipschitz functions, and solution finding.

Ordinary differential equations

Introduces ordinary differential equations of higher order and their solutions with initial conditions.

Vibratory Mechanics: Continuous Systems

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

Error Estimation in Numerical Methods

Explores error estimation in numerical methods for solving ordinary differential equations, emphasizing the impact of errors on solution accuracy and stability.

Homogeneous Differential Equations

Explores solving first-order homogeneous differential equations through variable changes and delves into the Bernoulli differential equation.

Ordinary Differential Equations: Separable Variables

Covers ordinary differential equations with separable variables and the conditions for unique solutions in EDOs.

Ordinary Differential Equations: Non-linear Analysis

Covers non-linear ordinary differential equations, including separation, Cauchy problems, and stability conditions.

Vibrating Strings: Mathematical Analysis and Fourier Series

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

Introduction to Ordinary Differential Equations

Introduces ordinary differential equations, their order, numerical solutions, and practical applications in various scientific fields.

Separable Differential Equations

Covers separable differential equations of order 1, defining separable equations and providing examples.

Differential Equations: Solution Methods

Explores the resolution of differential equations and the properties of exponential functions in electrical engineering.

Introduction to ODEs: System of 1st Order ODEs

Introduces Ordinary Differential Equations (ODEs) and their applications in physics, covering basics, initial value problems, and linear ODEs.

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.

Differential Equations: Existence and Uniqueness Theorems

Covers the existence and uniqueness of solutions for differential equations.