Mathematics 2 for Economics

Sommer semester 2024     

Working with mathematical models requires two skills: On the one hand one needs to be familiar with techniques for handling terms and formulæ and with methods for solving particular problems like finding extrema of a given function. Learning and applying such procedures is already part of the course Mathematical Methods. The second skill is the investigation of structural properties of a given model. One has to find conclusions that can be drawn from one's model and find convincing arguments for these.

In the first part of this course ( Mathematics 1: Linear Spaces and Metric Concepts) our emphasis has been on mathematical reasoning. which have been introduced in the framework of linear algebra.

In the second part we will use our skills and explore the second fundamental field of mathematics, analysis. There we often will try to replace non-linear functions locally by linear ones and apply our results from linear algebra. Besides dealing with the mathematical foundations of the procedures that are already well-known from the course Mathematical Methods we also will learn new methods. In particular we will be able to analyse dynamic systems.

In summary, the course covers the following topics:

• Sequences and Series
• Topology
• Derivatives
• Taylor Series
• Inverse and Implicit Function Theorem
• Convex Functions
• Static Optimization
• Integration
• Multiple Integrals
• Differential Equations
• Systems of Differential Equations
• Dynamic Optimization: Control Theory

Exercises

See Learning activities on the corresponding page at learn@wu.

Teaching/learning method(s)

The course is divided into three parts that interlace during the course:

1. Lectures, where the required material is presented by the supervisor.

   It is expected that students will read corresponding chapters in advance for each lecture!

2. Homeworks, where the students get familiar with the mathematical techniques.

3. Presentation of students' solution, where possible problems and common mistakes are discussed.

Assessment

See Syllabus on the corresponding page at learn@wu. It is expected that the students will do all their homeworks. This will be controlled by grading presentation of homework results (20%) as well as some quizzes (short intermediate tests, 80%).

The moving sum of credit points over 3 quizzes must not below 15 points to get a positive grade for the course.

	credit points	remark
Homework presentation	10 each	max 20
Quiz	10 each	max 80 (8 best of 11)
Sum	100	min 50 for positive grade

Learning Materials

• Lecture Notes Analysis and Dynamic Optimization (for oneside printing  |  for twoside printing)
• Introduction to Maxima for Economics
• Materials from course Mathematische Methoden (in German).
• Mathematics 1: Linear Spaces and Metric Concepts

Bibliography

• K. Houston: How to Think Like a Mathematician, Cambridge University Press, 2009.
• K. Sydsæter, P. Hammond, A. Seierstad, A. Strøm: Further Mathematics for Economic Analysis, Prentice Hall, 2005.
• K. Sydsæter, P. Hammond: Essential Mathematics for Economics Analysis, Prentice Hall, 3rd edition, 2008.
• A. C. Chiang, K. Wainwright: Fundamental Methods of Mathematical Economics, McGraw-Hill, New York, 2005

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Last change: Thu Feb 1 2024 by josef leydold