Linear Equations: Introduction and Solutions

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Linear Equations and Systems

Covers linear equations with multiple variables and systems, including solutions and consistency criteria.

General Solution Construction: Superposition Principle

Covers the construction of general solutions for differential equations using the superposition principle and emphasizes the uniqueness of solutions.

Linear Algebra: Systems of Linear Equations

Introduces linear algebra concepts, focusing on solving systems of linear equations and their representations.

Population Growth and Temperature Variation

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

Newton's Method: Convergence and Criteria

Explores the Newton method for non-linear equations, discussing convergence criteria and stopping conditions.

Cauchy Problem Resolution: Differential Equations Overview

Covers the resolution of a Cauchy problem for a first-order linear differential equation, detailing the construction of its general solution and the determination of initial conditions.

Numerical Analysis: Stability in ODEs

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

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Linear Differential Equations: General Solutions

Covers linear differential equations of the first order and methods of demonstration.

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.