Mathematics 4 - Further Mathematics for Physicists

SS 2020


Lectures: Monday and Thursday 13:00 - 14:30, Online (link to Zoom)

Tutorial classes: Friday 9:15 - 10:45, Online (link to Zoom)

Office hours: Tuesday 17:45 - 19:30, Online (link to Zoom)


Course in the Moodle system: link


The password to the online meetings can be found in AlmaWeb and Moodle


In order to be admitted to the exam, it is necessary to score at least 50% of total points



PREVIOUS COURSES MATH 1, MATH 2 and MATH 3


Web page of the course: Math 1, Math 2, Math 3



TOPICS


  • Introduction to Measure Theory: sigma algebras, measures, integration
  • Convergence theorems for integrals
  • Metric spaces
  • Normed and Banach spaces;
  • Bounded operators;
  • Hilbert spaces;
  • Fundamental theorems for Banach spaces;
  • Spectral theory of linear operators;
  • Compact and self-adjoint linear operators;
  • Introduction to differential geometry


    • BASIC LITERATURE


  • Anatolii Dorogovtsev "Elements of General Measure Theory and Integral"
  • Erwin Kreyszig "Introductory Functional Analysis with Applications"
  • Michael Reed, Barry Simon "Methods of Modern Mathematical Physics I: Functional Analysis"
  • Axel Schüler "Calculus 1 to 4"
  • Helmut Fischer, Helmut Kaulr "Mathematik für Physiker Band 2"
  • Erwin Kreyszig "Differential geometry"


    • ADDITIONAL LITERATURE


  • P. Halmos "Measure Theory"
  • H. Heuser "Lehrbuch der Analysis Teil 2", Vieweg+Teubner 2009
  • H. Heuser “Funktionalanalysis”, Teubner 2006
  • Barrett O'Neill "Elementary Differential Geometry"


    • EXAM


    Exam solutions



    LECTURE NOTES


    The link to video of my lectures can be found on AlmaWeb (in course materials) and Moodle


    Notes
    (This lecture notes mainly consist of the main material given during the lecture like definitions, statements, and examples)
    If you find any mistakes, please contact Raphael [dl18bewa at studserv.uni-leipzig.de] who is typing these lecture notes



    Handwritten lecture notes



    PROBLEM SHEETS


    Solutions of homework exercises have to be uploaded into the Moodle system (see "Solutions to Homework")


    Sheet 1 (by 22:00, Apr 22)

    Sheet 2 (by 22:00, Apr 29)

    Sheet 3 (by 22:00, May 6)

    Sheet 4 (by 22:00, May 13)

    Sheet 5 (by 22:00, May 20)

    Sheet 6 (by 22:00, May 27)

    Sheet 7 (by 22:00, June 3)

    Sheet 8 (by 22:00, June 10)

    Sheet 9 (by 22:00, June 17)

    Sheet 10 (by 22:00, June 24)

    Sheet 11 (by 22:00, July 1)

    Sheet 12 (by 22:00, July 8)

    Sheet 13 (by 22:00, July 15)


    Solutions

    If you have any questions or find any mistakes, please let me know.
    Solutions are written down by Maryna Konarovska [maryna.konarovska@gmail.com]