apl. Prof. Dr. Frank Werner

Otto-von-Guericke Universität Magdeburg

Institut für Mathematische Optimierung

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Summer 2017: Mathematical Methods II


New book for a refreshment of elementary mathematics:
      Frank Werner: A Refresher Course in Mathematics, Bookboon Publishers, May 2016, 284 pages
(Table of Contents;   Preface)
(this book is ad-supported and can be FREELY DOWNLOADED from the website of the publisher: download). The book contains 247 worked examples, 122 exercises for independent practicing and 62 figures. The solutions of the exercises can be downloaded here.


The inspection of the written examinations is possible on October 17, 2017 in building 02, room 215, from 10.00 a.m. to 12.00 a.m.


Thu 1.15 p.m. - 2.45 p.m. in G05-H4 (120)


M.Sc. Julia Lange: Wed 9.15 a.m. - 10.45 a.m. in G22A-216 (40) (group 1)
M.Sc. Julia Lange: Thu 3.15 p.m. - 4.45 p.m. in G22A-218 (40) (group 2)

Tutorials for practicing:

Ms. Greta Bartels: Mon 3.15 p.m. - 4.45 p.m. in G05-307 (40)

There are two hours of lectures and three hours of tutorials per week. Among the tutorials, there is a 2-hour traditional tutorial per week, where mainly the tutor presents solved exercises at the blackboard. In addition, there are two parallel 2-hour 'Tutorials for practicing', where mainly the students solve problems under guidance of the tutor and discuss solution strategies. It is recommended that each student attends every two weeks such a tutorial for practicing (either in an even or odd calendar week. Thus, for every student, there is one week with four hours of tutorials and the other week with two hours of tutorials.

Schedule of Tutorials


1. Vectors

2. Matrices

3. Systems of Linear Equations

4. Functions of Several Variables

Recommended textbook:

A textbook that includes all the topics from the lecture is available now (see Reference 1 below). The use of this textbook is STRONGLY recommended. Further information about the book can be found here.

Literature (Textbooks):

1) Werner, F.; Sotskov, Y.N.: Mathematics of Economics and Business, Routledge, Abingdon, New York, 2006 (free eBook download).

2) Sydsaeter, K.; Hammond, P.J.: Mathematics for Economic Analysis, Prentice Hall, 1995
(there also exists a German version).

3) Chiang, A.C.: Fundamental Methods of Mathematical Economics, Mc. Graw Hill, 1984.

4) Simon, C.P.; Blume, L.: Mathematics for Economists, W.W. Norton & Company, New York, London, 1994.

5) Opitz, O.: Mathematik, Lehrbuch für Ökonomen, Oldenbourg, 1990 (in German).

Exercises for the tutorials:

Below you find the complete list of exercises given at the end of Chapters 6 - 8 in the textbook by Werner and Sotskov. The exercises treated in the tutorials are a subset of these problems, and their numbers are given below in parentheses. These problems should be prepared by every student BEFORE the corresponding tutorial. The answers to these problems can be found on pages 486 - 510 of the textbook mentioned above (see Selected Solutions).

  • Chapter 6: pdf-File (Exercises 1 - 9b)

  • Chapter 7: pdf-File (Exercises 1, 3 - 10 and 14 - 17)

  • Chapter 8: pdf-File (Exercises 1 - 7 and 10 - 11)

  • Chapter 11: pdf-File (Exercises 1 - 5, 7 - 8, 10 - 11, 14 - 19, 21, 24 - 26 and 28)

  • Examinations:

    There is a one-hour written examination in Mathematical Methods II (in July). As working tools are allowed:

  • a pocket calculator according to the instructions of FWW and

  • EITHER ONE individually prepared ONE-SIDED sheet of paper with arbitrary material
        OR textbook `Mathematics of Economics and Business' by Werner and Sotskov

    Every student should indicate the chosen variant on the cover sheet of the examination paper ('1' stands for 'one page' and 'B' stands for 'book'). Note that the use of a collection of (handwritten or printed) copies of pages (of whatsoever) is NOT allowed.

    A selection of old (two-hour) examinations (in the related subject Mathematics II) including answers to the problems can be found under
    `Lehrmaterial' of the Faculty of Mathematics within the part `Klausuren'.

  • Past Examinations

    Examination July 2016 (pdf)

    I wish all students success in studying mathematical methods in business and economics!

    Quotation: If well used, books are the best of all things; if abused, among the worst.


    English version Last updated: 3 Oct 2017