Mathematics 3 - Vector Calculus and Partial Differential Equations

WS 2019/20


Lectures: Monday 15:15 - 16:45, Kleiner Hörsaal 281; Tuesday 09:15 - 10:45, Theoretischer Hörsaal 294 (Linnestraße 5)

Tutorial classes: Friday 13:30 - 15:00, Kleiner Hörsaal 281(Linnestraße 5) by Sayed Mohammad Reza Hashemi [hashemi at math.uni-leipzig.de]

Office hours: Thursday 17:00 - 18:30, Office A 327, Augusteum, Mathematisches Institut, Augustusplatz 10


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



PREVIOUS COURSES MATH 1 and MATH 2


Web page of the course: Math 1, Math 2



TOPICS


  • Integration in R^n: domain, line and surface integrals;
  • Gradient, divergence and curl;
  • Gauss's divergence, Green's and Stoke's theorems;
  • Holomorphic functions;
  • Complex line integral;
  • Laurent series;
  • Residues;
  • Heat, wave and Laplace equations;
  • Fourier transform


  • BASIC LITERATURE


  • Axel Schüler "Calculus 1 to 4"
  • Artem Sapozhnikov "Lecture notes, Part I (Math 3)"
  • Vladimir Zorich "Mathematical Analysis II"
  • B.V. Shabat "Introduction to Complex Analysis"
  • A. N. Tikhonov, A. A. Samarskii "Equations of Mathematical Physics"


  • ADDITIONAL LITERATURE


  • H. Heuser "Lehrbuch der Analysis Teil 1", 17. Auflage, Vieweg+Teubner 2009
  • H. Fischer, H. Kaul "Mathematik für Physiker, Band 1 and 2: Grundkurs", Vieweg+Teubner 2011
  • Walter Rudin "Principles of Mathematical analysis"
  • Gregory P Dresden, Brian Bradie, Jon Rogawski "Student Solutions Manual Multivariable Calculus"


  • EXAM


    Exam solutions


    Results of the exam are available on AlmaWeb (see Material for the complete course)

    You can see your works in my office between 16:00 and 18:00 on Friday, February 7



    LECTURE NOTES


    Notes
    (These are lecture notes which mainly consist of 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


    Sheet 1 (by 16:45, Oct 28)

    Sheet 2 (by 16:45, Nov 4)

    Sheet 3 (by 16:45, Nov 11)

    Sheet 4 (by 16:45, Nov 18)

    Sheet 5 (by 16:45, Nov 25)

    Sheet 6 (by 10:45, Dec 3)

    Sheet 7 (by 16:45, Dec 9)

    Sheet 8 (by 16:45, Dec 16)

    Sheet 9 (by 10:45, Jan 7)

    Sheet 10 (by 16:45, Jan 13)

    Sheet 11 (by 16:45, Jan 20)

    Sheet 12 (by 16:45, Jan 27)

    Sheet 13 for bonus points (by 18:30, Jan 30)


    Homework exercises Please pay your attention on marked exercises. Similar ones could be at the exam


    Grades (Homework 1-13)

    If you have any questions about your grades, please contact Maryna Konarovska [maryna.konarovska@gmail.com] who corrects all homework, or me