Mathematical techniques 3

Course goals

Course goals

1. Grasp the basic theory of ordinary differential equations, and apply it to solve first and second order ODEs and systems of ODEs.
2. Get acquainted with the notion of power series and apply it in practice to solve differential equations. 
3. Be able to use separation of variables to solve examples of partial differential equations arising in physics.
4. Learn examples of inner product spaces and eigenvalue problems. Grasp the basic theory of Fourier series and Fourier transform, apply it in computations and as a tool to solve partial differential equations.
5. Learn how the Dirac delta function is defined, what are its basic properties and how to use it in practice.

Content

Content
This course serves as a steppingstone towards advanced topics in physics. It provides a selection of methods for solving differential equations. In particular it covers power series and separation of variable methods, as well as a range of topics related to Fourier analysis including inner product spaces, eigenvalues and eigenvectors, Fourier series and Fourier transform, convolution, and elements of distribution theory (the Dirac delta function).