Functional Analysis uses concepts of the basic Linear Algebra courses such as vector space, linear operator, dual space, scalar product, adjoint map, eigenvalue, spectrum, in order to solve equations in infinite-dimensional function spaces, in particular linear differential equations.

The algebraic notations have to be extended by topological concepts such as convergence, completeness and compactness. This approach was only developed at the beginning of the 20th century, but nowadays it belongs to the methodological basis in Analysis, Numerics and Mathematical Physics, especially in Quantum Mechanics.

We will focus on the aspects of the theory which are relevant for the theory of Partial Differential Equations.

**Exercise Sheets**

There will be one exercise sheet every week with three or four problems. You can hand in your solution of the two exercises which are labeled with a 'C' and then the tutor will correct it.

In the problem class we will discuss the solutions. If I have not enough time, I will upload my sketches to the missing problems here on the webpage.

1. Exercise Sheet Solutions to 1. Exercise Sheet

2. Exercise Sheet Solutions to 2. Exercise Sheet

3. Exercise Sheet Solutions to 3. Exercise Sheet

4. Exercise Sheet Solutions to 4. Exercise Sheet

5. Exercise Sheet

6. Exercise Sheet

7. Exercise Sheet Solutions to 7. Exercise Sheet

8. Exercise Sheet Solutions to 8. Exercise Sheet

9. Exercise Sheet Solutions to 9. Exercise Sheet

10. Exercise Sheet Solutions to 10. Exercise Sheet

11. Exercise Sheet Solutions to 11. Exercise Sheet

12. Exercise Sheet Solutions to 12. Exercise Sheet (Exercise 2 is now correct)

13. Exercise Sheet Solutions to 13. Exercise Sheet

14. Exercise Sheet

# Examination

There will be a written exam and two possible dates, you can choose your favourite day:

Exam 1.: 21.02.2017 at 09.00 - 11.00 o'clock in Hertz-Hoersaal (Geb. 10.11)

Exam 2.: 12.04.2017 at 09.00 - 11.00 o'clock in SR 1.067 (Math Buildung)

**Post-exam review:**

If someone is interested in his or her exam, please come in my office (2.033/2.034) next week (08.05.-12.05.).

# References

- Alt, H.W.: Linear Functional Analysis
- Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations
- Hirzebruch, F. ,Scharlau, W.: Einführung in die Funktionalanalysis
- Rudin, W.: Functional Analysis