Vitalii_Konarovskyi

Mathematics 1 - Linear Algebra and Calculus of Functions of One Variable (10-PHY-BIPMA1)

WS 2018/2019


Lectures: Monday 09:15 - 10:45 and Wednesday 09:15 - 10:45, Theoretischer Hörsaal (Linnestraße 5)

Tutorial classes for Group A: Wednesday 17:00 - 18:30, Theoretischer Hörsaal (Linnestraße 5) by Dr. Michael Schnurr [michael.schnurr at mis.mpg.de]

Tutorial classes for Group B: Thursday 7:30 - 9:00, Theoretischer Hörsaal (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



TOPICS


  • Convergence of sequences and series;
  • Continuous functions;
  • Differential calculus for functions of a single variable;
  • Integration of functions of a single variable;
  • Basic concepts of linear algebra, groups, matrix arithmetic


    • BASIC LITERATURE


  • Kenneth A. Ross "Elementary Analysis: The Theory of Calculus", 2nd ed., Springer 2013
  • I. Lankham, B. Nachtergaele, A. Schilling "Linear Algebra As An Introduction To Abstract Mathematics", WSPC, 2016


    • ADDITIONAL LITERATURE


  • Axel Schüler "Calculus 1 to 4"
  • 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


    • EXAM


    An example of problem sheet for the exam (Solutions will be discussed during the lecture on Wednesday Feb 6)

    List of exercises for the exam

    See also exams and their solutions from last years:
        Exam 2018, Retake 2018, Exam 2017, Retake 2017, Exam 2016, Retake 2016, Exam 2015, Retake 2015



    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)

    You may see your works in my office between 16:30 and 18:00 on Monday February 25


    Retake solutions


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

    You may see your works in my office between 16:00 and 17:00 on Wednesday April 17



    LECTURE NOTES


    Note 1 (Oct 15)

    Note 2 (Oct 17)

    Note 3 (Oct 22)

    Note 4 (Oct 24)

    Note 5 (Oct 29)

    Note 6 (Nov 5)

    Note 7 (Nov 7)

    Note 8 (Nov 12)

    Note 9 (Nov 14)

    Note 10 (Nov 19)

    Note 11 (Nov 26)

    Note 12 (Nov 28)

    Note 13 (Dec 5)

    Note 14 (Dec 10)

    Note 15 (Dec 12)

    Note 16 (Dec 17)

    Note 17 (Dec 19)

    Note 18 (Jan 7)

    Note 19 (Jan 9)

    Note 20 (Jan 14)

    Note 21 (Jan 16)

    Note 22 (Jan 21)

    Note 23 (Jan 23)

    Note 24 (Jan 28)


    Notes (full course) (Oct 15 - Jan 28)



    PROBLEM SHEETS


    Sheet 1 (by 10:45, Oct 29)

    Sheet 2 (by 10:45, Nov 7)

    Sheet 3 (by 10:45, Nov 14)

    Sheet 4 (by 10:45, Nov 19)

    Sheet 5 (by 10:45, Nov 28)

    Sheet 6 (by 10:45, Dec 5)

    Sheet 7 (by 10:45, Dec 12)

    Sheet 8 (by 10:45, Dec 19)

    Sheet 9 (by 10:45, Jan 9)

    Sheet 10 (by 10:45, Jan 16)

    Sheet 11 (by 10:45, Jan 23)

    Sheet 12 (by 10:45, Jan 30)

    Sheet 13 (by 10:45, Feb 4)

    Sheet 14 (by 10:45, Feb 6)


    Grades (Homework 1-14)



    COURSE JOURNAL


  • Oct 15 - Elements of Set Theory and Mathematical Induction
  • Oct 17 - Completeness of the Set of Real Numbers and some Inequalities
  • Oct 22 - Convergence of Sequences: Notion of Limit and some Limit Theorems for Sequences
  • Oct 24 - Subsequences and Monotone Sequences
  • Oct 29 - Cauchy Sequences and Base Notion of Functions
  • Nov 5 - Limits of Functions
  • Nov 7 - Properties of Limits of Functions and One-Sided Limits
  • Nov 12 - Continuous Functions
  • Nov 14 - Properties of Continuous Functions
  • Nov 19 - Differentiation
  • Nov 26 - Derivatives of Inverse Functions and some Theorems
  • Nov 28 - Application of Derivatives
  • Dec 5 - L'Hospital's Rule and Taylor's Theorem
  • Dec 10 - Local Extrema of Function
  • Dec 12 - Antiderivative and Indefinite Integral
  • Dec 17 - Riemann Integral
  • Dec 19 - Fundamental Theorem of Calculus and Application of Riemann Integral
  • Jan 7 - Improper Integrals
  • Jan 9 - Elementary Properties of Series and Series with Positive Terms
  • Jan 14 - Series with Arbitrary Terms
  • Jan 16 - Complex Numbers
  • Jan 21 - Fundamental Theorem of Algebra and Vector Spaces
  • Jan 23 - Vector Subspaces and Linear Span
  • Jan 28 - Basis
  • Jan 30 - Linear Maps
  • Feb 4 - Matrices