Differential Equations

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Chapter 1 - FIRST ORDER DIFFERENTIAL EQUATIONS

1.1. Introduction

1.2. Elementary methods

1.3 Other kinds of equations

1.4. Applications

Chapter 2 - LINEAR EQUATIONS OF HIGHER ORDER

2.1 Second order linear equations

2.2 Linear equations of order n

2.3 Applications

Chapter 3 - LAPLACE TRANSFORM

3.1 Definition and basic properties

3.2 Resolution of equations and linear systems

3.3 Advanced properties

Chapter 4 - METHOD OF SEPARATION OF VARIABLES

4.1 Introduction to partial differential equations

4.2 Method of separation of variables

4.3 Fourier series

4.4 More examples of separation of variables

Chapter 5 - STURM-LIOUVILLE PROBLEMS

5.1 Introduction

5.2 Generalized Fourier series

5.3 Rayleigh quotient and Minimization Principle

5.4 Bessel equation

Chapter 6 - FOURIER TRANSFORM

6.1 Fourier transform on the real line

6.2 Resolution of equations with the Fourier transform

6.3 Fourier transform in several variables