This is the first part of a 2 semester course covering mathematical methods of wide use in physics and engineering. We will have a strong focus on Applied Functional Analysis, i.e., modern mathematical tools of infinite dimensional linear algebra for the study of differential and integral operators.
Over the two semesters, we will discuss metric spaces, Banach and Hilbert spaces, Lp and Sobolev spaces, linear operators, spectral theory, and differential operators. Furthermore we will discuss some methods from the calculus of variations and their relation to finding solutions of (non-linear) partial differential equations.
Audience: The course is aimed at students from the sciences (e.g., physicists who are tired of the usual handwaving arguments from their quantum mechanics courses) and engineering who would like to get a solid understanding of the relevant modern mathematical tools needed in their fields and at students from mathematics.
Prerequisites: A solid background in advanced calculus and ordinary differential equations. Do not hesitate to contact me in case there are any questions.
Homework:
| Homework 1: | HW 1: | Due Friday 11 September 2009 |
| Homework 2: | HW 2: | Due Monday 28 September 2009 |
| Homework 3: | HW 3: | Due Wednesday 14 October 2009 |
| Homework 3: | HW 4: | Due Monday 30 November 2009 |
Script: