Lectures related to Differential Equations: Solution Methods

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

Covers linear differential equations of order n with constant coefficients and how to find their general solutions.

Differential Equations: Speed Variation Analysis

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

Differential Equations: General Solutions and Methods

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

Linear Differential Equations

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

Material Point Model: Basics

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

General Solution of Homogeneous Second Order Linear Differential Equations

Covers the general solution of homogeneous second-order linear differential equations with constant coefficients and the concept of linear independence of solutions.

Direction Fields, Euler Methods, Differential Equations

Explores direction fields, Euler methods, and differential equations through practical exercises and stability analysis.

Second Order Equations: Solutions Construction

Covers constructing solutions for second-order differential equations with a given second member through linear combinations of known solutions.

Numerical Integration: Euler Method

Covers the progressive Euler method for numerical integration of ODEs, including Cauchy problems and Runge-Kutta methods.

Numerical Methods for ODEs: Crank-Nicolson, Heun, Euler, RK4

Explores numerical methods like Crank-Nicolson, Heun, Euler, and RK4 for solving ODEs, emphasizing error estimation and convergence.

Ordinary Differential Equations: Non-linear Analysis

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

Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

Canonical Transformations: Existence and Equations

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

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.

Linear Differential Equations: Second Order with Constant Coefficients

Covers linear differential equations of the second order with constant coefficients, focusing on solution methods for various discriminant cases.

Multistep methods

Covers multistep methods for solving differential equations, focusing on stability conditions and examples.

Homogeneous Differential Equations

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

Homogeneous Solutions: Linear Independence

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

Differential Equations: Methods and Solutions

Discusses methods for solving first-order linear differential equations, focusing on separation of variables and the integrating factor method.