Differential Equations
Syllabus
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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