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 theoryExam 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).