Lectures related to Ordinary Differential Equations: Definitions and Examples

Linear Differential Equations: Homogeneous and Separable

Covers linear differential equations of order 1, focusing on homogeneous and separable equations.

Explores finding solutions of differential equations, emphasizing maximal solutions and general solutions with constants.

Differential Equations: General Solutions and Methods

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.

Material Point Model: Basics

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

Population Growth and Temperature Variation

Explores population growth models and temperature variation equations, focusing on differential equations and solution methods.

Canonical Transformations: Existence and Equations

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

One Dimensional Harmonic Oscillator

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

Differential Equations: Modeling Physical and Biological Phenomena

Covers differential equations and their applications in modeling various phenomena.

Separable Differential Equations

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

Solving Separable Equations

Covers the method for solving separable equations and linear homogeneous equations, as well as a simple population growth model.

Differential Equations: Implicit Solutions

Explores implicit solutions for differential equations and their applications in different scenarios.

Canonical Transformations: Hamilton-Jacobi Equation

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

Advanced Analysis II: Differential Equations and Timers

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

General Solutions of Differential Equations

Explores general solutions of differential equations with a focus on x

Differential Equations: Existence and Uniqueness Theorems

Covers the existence and uniqueness of solutions for differential equations.

Differential Equations: Solutions and Monotonicity

Explores solutions of differential equations and their monotonicity properties.

Linear Differential Equations

Explores linear differential equations, including higher-order linear homogeneous equations and equations with constant coefficients.

Partial Derivatives and Differential Equations

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

Numerical Analysis: Stability in ODEs

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

Advanced Analysis: Differential Equations Overview

Provides an overview of differential equations, their properties, and methods for finding solutions through various examples and graphical representations.