## Mathematics 2 for Economics

### Sommer semester 2019

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 Mathematische Methoden. 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 Mathematische Methoden 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 Lernaktivitäten 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.

### 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

Last change: Fri Feb 22, 2019 by josef leydold 