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MATHEMATICAL METHODS OF PHYSICS WS 19/20

Lectures: Tue 12:00-14:00 T2-205, Thu 12:00-14:00 T2-205
Tutorials: TBA

Instructor: Jun.-Prof. Dr. Soeren Schlichting
(sschlichting AT physik.uni-bielefeld.de)

Tutors: Felix Ziesche
( fziesche AT physik.uni-bielefeld.de)
Stefan Kleine Bruening
( skbruening AT physik.uni-bielefeld.de)

This undergraduate (B.Sc.) level course teaches mathematical methods for physicists in preparation for standard and advanced Theoretical Physics lectures and research.

Topics include:

- Complex calculus
- Function spaces & distributions
- Operators & Spectral theory

Exam scores -- 1st Exam

Score distribution || Grade distribution

Student evaluation of the course

Course materials and exercise sheets will be posted over the course of the semester

Exercise sheets:

Exercise Sheet 1 -- Oct 15th || Solution

Exercise Sheet 2 -- Oct 22nd || Solution

Exercise Sheet 3 -- Oct 29th || Solution

Exercise Sheet 4 -- Nov 05th || Solution

Exercise Sheet 5 -- Nov 12th || Solution

Exercise Sheet 6 -- Nov 19th || Solution

Exercise Sheet 7 -- Nov 26th || Solution

Exercise Sheet 8 -- Dec 03rd || Solution

Exercise Sheet 9 -- Dec 10th || Solution

Exercise Sheet 10 -- Dec 17th || Solution

Exercise Sheet 11 -- Jan 07th || Solution

Exercise Sheet 12 -- Jan 14th || Solution

Exercise Sheet 13 -- Jan 21st || Solution

Exercise Sheet 14 -- Jan 28th|| Solution

Course materials:

Week 1 -- Komplexe Zahlen & Funktionen
Notes from Oct 8th and Notes from Oct 10th

Week 2 -- Komplexe Differenzierbarkeit
Notes from Oct 15th and Notes from Oct 17th

Week 3 -- Komplexe Kontourintegrale & Stammfunktionen
Notes from Oct 22nd and Notes from Oct 24th

Week 4 -- Cauchy's Integralsatz & Cauchy's Integralformel
Notes from Oct 29nd and Notes from Oct 31st

Week 5 -- Potenz/Laurentreihen & Singularitaten
Notes from Nov 05th and Notes from Nov 07th

Week 6 -- Satz von Liouville & Residuensatz
Notes from Nov 12th and Notes from Nov 14th

Week 7 -- Residuen,Partialbruchzerlegung & reelle Integrale
Notes from Nov 19th and Notes from Nov 21st

Week 8 -- Reelle Integrale & Integrale mit Singulartaeten
Notes from Nov 26th and Notes from Nov 28th

Week 9 -- Kramers-Kronig Relation & Sattelpunktsnaeherung
Notes from Dec 3rd and Notes from Dec 5th

Week 10 -- Vektorraum, Basis & Dualraum
Notes from Dec 10th and Notes from Dec 12th

Week 11 -- Funktionenraeume, Dirac Distribution, Fourierreihen
Notes from Dec 17th and Notes from Dec 19th

Week 12 -- Fourierreihen und Fouriertransformation
Notes from Jan 07th and Notes from Jan 09th

Week 13 -- Fouriertransformation und Green's Funktionen
Notes from Jan 14th and Notes from Jan 16th

Week 14 -- Laplacetransformation & Inverse Laplacetransformation
Notes from Jan 21st and Notes from Jan 23rd

Week 15 -- Differentialgleichungen via Laplacetransformation, Operatoren
Notes from Jan 28th and Notes from Jan 30th

Literature:

Books listed below are available in the university library as part of the Semesterapparat.
- Jaenich, Klaus : Analysis für Physiker und Ingenieure
- von Mangoldt, Hans : Hoehere Mathematik 4
- Courant, Richard : Introduction to calculus and analysis 1 & 2
- Smirnov, Vladimir I : Lehrgang der höheren Mathematik 1,2 & 3
- Arfken, George B. : Mathematical methods for physicists
- Dennery, Philippe : Mathematics for physicists
- Kerner, Hans : Mathematik für Physiker
- Fischer, Helmut : Mathematik für Physiker 1&2
- Morse, Philip McCord : Methods of theoretical physics 1&2

Besides the above literature, students are also encouraged to consult mathematical textbooks on complex calculus (Funktionentheorie).