AUM CH 4.6- Part 1 : Variation of Parameters شرح

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محتوى الماده الذي تم شرحه في الفيديوهات هو

Chapter 1: Introduction

1.1: Introduction to Differential Equations (Classification, Order, Linearity)

1.2: Initial-Value Problems

Chapter 2: First-Order Differential Equations

2.1: Solution Curves Without a Solution (Direction Fields, Phase Lines)

2.2: Separable Differential Equations

2.3: Solving First-Order Linear Differential Equations (Integrating Factors)

2.4: Exact Differential Equations

2.5: Solutions by Substitutions (Bernoulli’s Equation, Homogeneous Forms)

2.6: Numerical Methods (Euler’s Method)

Chapter 3: Modeling with Differential Equations

3.1: Linear Models (Applications in Growth/Decay Models)

3.2: Nonlinear Models

Chapter 4: Higher-Order Linear Differential Equations

4.1.1: Initial-Value and Boundary-Value Problems

4.1.2: Homogeneous Linear Equations

4.1.3: Nonhomogeneous Linear Equations

4.2: Reduction of Order

4.3: Homogeneous Equations with Constant Coefficients (Characteristic Equation)

4.6: Variation of Parameters (General Solutions)
4.7: Cauchy Euler Equations

4.9: Solving Systems of Linear DEs by Elimination

Chapter 7: Laplace Transforms

7.1: Definition and Basic Properties

7.2: Inverse Transforms and Transforms of Derivatives

7.3-7.4: Operational Properties (Translation, Convolution)

7.5: The Dirac Delta Function