apl. Prof. Dr. Frank Werner

Otto-von-Guericke Universität Magdeburg

Institut für Mathematische Optimierung

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Winter 2020/21: Mathematical Methods I

New: Examination in Winter term 2020/21

The exam will be ONLINE. This exam will take place at the scheduled date

MARCH 29, 2021, 11.00 a.m. - 12.00 a.m.

You will get all necessary information per email before March 15. I will also still overtake the correction of your written assignments.
Link for the exam:   Link

Please do NOT send separately emails (there are 139 registrations for this exam ...).

The check of the examinations will be completed by the end of April. For students who do not pass (less than 20 points), it is NOT counted as a failure (only identified attempts to deceive are graded as 5). So, only assigned grades will be published.

New: E-Learning link

All Zoom information can be found (additionally)   here   (login required).

New: Winter term 2020/21

ALL lectures and tutorials will be held ONLINE via Zoom. A registration to the course via LSF is required. In the lectures, I refer to our textbook 'Mathematics of Economics and Business' which can be FREELY DOWNLOADED as an ebook from the publisher's website or from all Amazon Kindle stores (see the information below about 'Recommended textbook'). There exists also a booklet 'A Refresher Course in Mathematics', which can also be FREELY DOWNLOADED from the Bookboon publisher's website (see also information below).

New: Refresher Course

New book for a refreshment of elementary mathematics:
      Frank Werner: A Refresher Course in Mathematics, Bookboon Publishers, May 2016, 284 pages
(September 2020: 4.9/5 from 26 evaluations)    (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 and 122 exercises for independent practicing (link for discussions). The solutions of the exercises can be downloaded here.
The questions of a multiple choice self-test related to the contents of the book can be found under MC self-test: questions, and the answers to the questions can be found under MC self-test: answers.


Wed 9.15 - 10.45 a.m. (ONLINE)


Mon 9.15 a.m. - 10.45 a.m. (group 1) (ONLINE)
Tue 1.15 p.m. - 2.45 p.m. (group 2) (ONLINE)

Tutorials for practicing:

Mr. Kirill Kukharenko: Wed 5.15 p.m. - 6.45 p.m. (ONLINE)
(odd calendar week: group 1; even calendar week: group 2)

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.


1. Logic, Sets and Real Numbers

2. Sequences and Series

3. Functions of a Real Variable

4. Differential Calculus for Functions of a Real Variable

5. Integration

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 1 - 5 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 1 - 5, 8 - 16 and 23 - 29)

  • Chapter 2: pdf-File (Exercises 1 - 9)

  • 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)

    For a detailed schedule of the tutorials see here (pdf-File)


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

  • a pocket calculator according to the instructions of FWW and

  • EITHER ONE individually prepared ONE-SIDED A4 sheet of paper with arbitrary material
        OR textbook `Mathematics of Economics and Business' by Werner and Sotskov

    The used material may not contain solved problems from tutorials, lectures and old exams. 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) including the Ebook is NOT allowed. If the formula sheet is used, please add your name and matriculation number and hand it in together with your examination

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

    Past exam questions classified by topics

  • Selected Past Examinations (1 hr)

    Examination February 2020 (pdf)

    Retake Examination July 2018 (pdf)

    Examination February 2018 (pdf)

    Retake Examination July 2016 (pdf)

    Examination February 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: 16 Apr 2021