##
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