Lectures related to Variation of parameters

Scalar Linear 2nd Order ODEs: Obtaining Particular Solution

Covers the variation of parameters method to obtain particular solutions to inhomogeneous ODEs.

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

Covers second-order linear differential equations and their solutions, including the method of variation of constants.

General Solution of Homogeneous Differential Equations

Explores the theory of solutions for linear differential equations, covering uniqueness, variation of constants, and non-uniqueness.

General Solutions of Differential Equations

Covers finding general solutions for differential equations using various methods and concepts, including explicit and implicit forms, integration constants, and intermediate hypotheses.

Conformal Transformations: Theory and Applications

Explores the theory and applications of conformal transformations, covering special conformal transformations and isomorphic transformations.

EDOL1: Inhomogeneous Case

Covers the analysis of second-order linear differential equations with constant coefficients in the inhomogeneous case.

Scalar Linear Higher Order ODEs: Properties and Solutions

Explores properties and solutions of scalar linear higher order ODEs with x-dependent coefficients and constant coefficients.

Linear Differential Equations

Covers linear differential equations and methods to find solutions with examples.

Characteristic Polynomials and Solutions

Covers characteristic polynomials, roots, and associated solutions for differential equations.

Homogeneous Differential Equations

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

Advanced Analysis II: Resonant Cases and Variable Coefficients

Covers resonant cases, variable coefficients, and methods for solving differential equations.

General Integrals: Notation and Equations

Covers the general concept of integrals, focusing on notation and equations.

Frobenius Method: Introduction

Introduces the Frobenius method for solving second-order linear ODEs around ordinary points.

Population Growth and Temperature Variation

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

Inhomog 2nd order B

Covers the solution of inhomogeneous second-order differential equations.

Linear Differential Equations: Second Order with Constant Coefficients

Covers the definitions and solutions of linear differential equations of the second order with constant coefficients.

Bessel Equation: Introduction

Introduces the Bessel equation and systematic methods for solving scalar linear 2nd order ODEs, with practical examples of eigenmodes of vibration.

Solving Differential Equations with Bernoulli's Equation

Covers solving differential equations using Bernoulli's equation and variable transformations to simplify linear inhomogeneous forms.

Linear Differential Equations

Covers the solution of linear differential equations of the first order, both homogeneous and inhomogeneous cases.