Mathematics 2 - Calculus of Functions of More Than One Variable

SS 2019


Lectures: Monday 09:15 - 10:45 and Wednesday 11:00 - 12:30, Kleiner Hörsaal 281(Linnestraße 5)

Tutorial classes for Group A: Friday 13:30 - 15:00, Kleiner Hörsaal 281(Linnestraße 5) by Mahsa Sayyary [mahsa.sayyary at mis.mpg.de]

Tutorial classes for Group B: Wednesday 13:30 - 15:00, Seminarraum SR 218(Linnestraße 5) by Ikhwan Khalid [ikhwankhalid92 at gmail.com]

Office hours: Friday 16:30 - 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 COURSE MATH 1


Full course

Web page of the course



TOPICS


  • Linear Maps and Matrices;
  • Eigenvalues and Eigenvectors;
  • Inner Product Spaces;
  • Bilinear Forms;
  • Functions of Several Variables;
  • Differential Calculus of Functions of Several Variables;
  • Extrema of Functions of Several Variables;
  • Ordinary Differential Equations


  • BASIC LITERATURE


  • Axel Schüler "Calculus 1 to 4"
  • Walter Rudin "Principles of Mathematical analysis"
  • I. Lankham, B. Nachtergaele, A. Schilling "Linear Algebra As An Introduction To Abstract Mathematics", WSPC, 2016
  • K. Hoffman, R. Kunze "Linear Algebra"
  • William F. Trench "Elementary Differential Equations with Boundary Value Problems"


  • ADDITIONAL LITERATURE


  • H. Heuser "Lehrbuch der Analysis Teil 1", 17. Auflage, Vieweg+Teubner 2009
  • S. Bosch "Lineare Algebra", 4. Auflage, Springer 2008
  • H. Fischer, H. Kaul "Mathematik für Physiker, Band 1: Grundkurs", Vieweg+Teubner 2011
  • A. Kurosh "Higher Algebra"
  • Gregory P Dresden, Brian Bradie, Jon Rogawski "Student Solutions Manual Multivariable Calculus"
  • William F. Trench "Introduction to Real Analysis"
  • William F. Trench "Student Solutions Manual for Elementary Differential Equations with Boundary Value Problems"


  • EXAM


    List of admitted students is available on Almaweb (see Material for the complete course)

    Exam solutions

    Results of the exam are available on Almaweb (see Material for the complete course). Your grades will be announced after the correction of all homework approximately until July 26

    You may see your works in my office between 14:00 and 16:00 on Friday, July 19


    Retake solutions



    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
    (Full version of the notes)



    PROBLEM SHEETS


    Sheet 1 (by 12:30, Apr 17)

    Sheet 2 (by 12:30, Apr 24)

    Sheet 3 (by 10:45, Apr 29)

    Sheet 4 (by 10:45, May 6)

    Sheet 5 (by 10:45, May 13)

    Sheet 6 (by 10:45, May 27)

    Sheet 7 (by 15:00, May 31)

    Sheet 8 (by 12:30, June 5)

    Sheet 9 (by 12:30, June 12)

    Sheet 10 (by 12:30, June 19)

    Sheet 11 (by 12:30, June 26)

    Sheet 12 (by 12:30, July 3)

    Sheet 13 (by 10:45, July 8)

    Sheet 14 (by 12:30, July 10)


    Grades (Homework 1-13)

    Because of the short period of time before the exam, homework 14 was evaluated only for students whose points were between 35-49%. The homework of other students will be graded later.

    If you have any questions about your grades, please, contact Ikhwan Khalid [ikhwankhalid92 at gmail.com] who corrects all homework



    COURSE JOURNAL


  • Apr 1 - Systems of linear equations
  • Apr 3 - Vector spaces
  • Apr 5 - Invertible matrices
  • Apr 15 - Rank of matrices
  • Apr 17 - Fundamental system of solutions
  • Apr 24 - Determinant
  • Apr 29 - Change of basis
  • May 6 - Eigenvalues and eigenvectors
  • May 8 - Inner product
  • May 10 - Orthonormal basis
  • May 13 - Orthonormal projections
  • May 14 - Adjoint operators
  • May 15 - Unitary operators
  • May 27 - Bilinear forms
  • May 29 - Topology on R^d
  • May 31 - Functions of several variables
  • June 3 - Continuous functions
  • June 5 - Differentiable functions
  • June 12 - Differentiable functions II
  • June 17 - Implicit function theorem and higher order derivatives
  • June 19 - Local extrema of functions
  • June 24 - Conditional local extrema
  • June 26 - Basic concept of differential equations
  • July 1 - First order differential equations
  • July 3 - Existence and uniqueness of solutions. Higher order linear differential equations
  • July 8 - Systems of linear differential equations