apl. Prof. Dr. Frank Werner

Otto-von-Guericke Universität Magdeburg

Institut für Mathematische Optimierung

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Winter 2014/15: Mathematical Methods in Business & Economics


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 inspection of the written examinations is possible on April 20, 2016 in building 02, room 215, from 1.30 p.m. to 3.30 p.m.


Thu 3.15 - 4.45 p.m. in G05 - H4 (120)
Fri 1.15 - 2.45 p.m. in G05 - H4 (120)


M.Sc. Julia Lange: Tue 3.15 p.m. - 4.45 p.m. in G02-311 (72) (CHANGE) and
M.Sc. Julia Lange: Thu 11.15 a.m. - 12.45 p.m. in G05-117 (40)

Every student should attend one of the tutorials per week (preferably each week on the same day). It is recommended that all subgroups in the weekly tutorials have approximately the same size.


1. Logic, Sets and Real Numbers

2. Sequences, Series, Finance

3. Functions of a Real Variable

4. Differential Calculus for Functions of a Real Variable

5. Integration

6. Vectors

7. Matrices and Determinants

8. Systems of Linear Equations

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.

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 1 - 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 1: pdf-File (Exercises 2, 4 - 5, 8 - 16 and 23 - 29)

  • Chapter 2: pdf-File (Exercises 1 - 20)

  • Chapter 3: pdf-File (Exercises 6 - 9 and 11 - 13)

  • Chapter 4: pdf-File (Exercises 1 - 16, 17b-c without remainder, and 20)

  • Chapter 5: pdf-File (Exercises 1 - 5 and 7a)

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

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

  • Chapter 8: pdf-File (Exercises 1 - 6 and 11)

  • Examinations:

    There is a two-hour written examinations in Mathematical Methods in Economics and Business (in February). As working tools are allowed:

  • a pocket calculator according to the instructions of FWW and

  • EITHER TWO individually prepared ONE-SIDED sheets 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 ('2' stands for 'two pages' 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 examinations (in the related subjects Mathematics I and Mathematics II) including answers to the problems can be found under
    `Lehrmaterial' of the Faculty of Mathematics within the part `Klausuren'.

  • Some Past Examinations (2 hs)

    Retake Examination July 2015 (pdf)

    Examination February 2015 (pdf)

    Retake Examination July 2014 (pdf)

    Examination February 2014 (pdf)

    Retake Examination August 2013 (pdf)

    Examination February 2013 (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: 10 Apr 2016