Differential Equations
Lecture notes
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Chapter 1.
The chapter is dedicated to the resolution of first order differential equations and their applications.
Chapter 2.
We present resolution methods for linear equations of order higher than one, including cases of constant and variable coefficients.
Chapter 3.
3. Laplace transform (PDF).
We define this useful tool and apply it to the resolution of a very wide spectrum of equations and systems of equations.
Chapter 4.
This chapter studies partial differential equations with the mentioned method. As a necessary tool we also study Fourier series.
Chapter 5.
5. Sturm-Liouville problems (PDF).
Here we extend the method of separation of variables to more general cases of eigenvalue problems.
Chapter 6.
6. Fourier transform (PDF).
We dedicate this final chapter to a very powerful mathematical tool, the Fourier transform, and to its applications to the resolution of equations.