Advanced Mathematics for Economics (HS23)

• In the first part of this course we will give a review of linear algebra.
• In the second part  we look at functions and Taylor's formula.
• In the third part we study optimization problems (unconstrained and constrained).

Sydsaeter K., Hammond P., Seierstad A., Strom A.: Further Mathematics for Economic Analysis, Prentice Hall.Chiang,

Alpha C.: Fundamental Methods of Mathematical Economics, McGraw-Hill International Editions.

• Exercises can (not have to) be solved. If you hand in the solutions of all exercises then the solutions will be marked. All these marks together (arithmetic mean) give the preliminary mark. At the end of the term there will be an examination.
  Your overall mark will be
  • the arithmetic mean of the preliminary mark and the examination mark, if (arithmetic mean of the preliminary mark and the examination mark) > (examination mark)
  • the examination mark, otherwise
• If you do not hand in the solutions of the exercises, then your examination mark is your overall mark.

There is no compulsory attendance at all.

Date, time and place of the examination:
Monday, 09.10.2023, 13:30-15:00 in S14 (Seminarraum, WWZ)

Allowed electronic means:
simple pocket calculator (einfacher Taschenrechner, according to Merkblatt Hilfsmittel)

Allowed non-electronic means:
open-book

You can download a Mock examination.

Keywords
vector, matrix, eigenvalue, eigenvector, diagonalization, linear transformation, spectral theorem for symmetric matrices, quadratic forms and definitness

Not relevant for examination
generalized eigenvalues

Preparation
Please study the following Handout 1.

Exercises
Please solve the following problems and hand in your solutions of the marked questions by 25.09.2023 at the latest.

Timetable
Mo, 04.09.23, 09:15-12:00 (Seminarraum S5, Juristische Fakultät)
1. Part Theoretical foundations (presentation of the handout): vector, matrix, eigenvalue, eigenvector
2. Part Self-study (of the handout), questions and work on the exercises

Tue, 05.09.23, 09:15-12:00 (Seminarraum S5, Juristische Fakultät)
1. Part Theoretical foundations (presentation of the handout): diagonalization, spectral theorem for symmetric matrices
2. Part Self-study (of the handout), questions and work on the exercises

We, 06.09.23, 09:15-12:00 (Seminarraum S5, Juristische Fakultät)
1. Part Theoretical foundations (presentation of the handout): quadratic forms
2. Part Self-study (of the handout), questions and work on the exercises

Keywords
partial derivative, gradient, Hesse matrix, differential, directional derivative, chain rule, implicit function theorem and derivative, Taylor formula, concave and convex functions, unconstrained optimization

Not relevant for examination
Quasi-concave and quasi-convex functions

Preparation
Please study the following Handout 2.

Exercises
Please solve the following problems and hand in your solutions of the marked questions by 25.09.2023 at the latest.

Timetable
Thu, 07.09.23, 09:15-12:00 (Seminarraum S5, Juristische Fakultät)
1. Part Theoretical foundations (presentation of the handout): partial derivative, gradient, Hesse matrix, differential, chain rule, implicit function theorem, directional derivative
2. Part Self-study (of the handout), questions and work on the exercises

Fri, 08.09.23, 09:15-12:00 (Seminarraum S5, Juristische Fakultät)
1. Part Theoretical foundations (presentation of the handout): Taylor formula, concave and convex functions
2. Part Self-study (of the handout), questions and work on the exercises

Mo, 11.09.23, 09:15-12:00 (Seminarraum S5, Juristische Fakultät)
1. Part Theoretical foundations (presentation of the handout): unconstrained optimization
2. Part Self-study (of the handout), questions and work on the exercises

Keywords
local and global extremal points, unconstrained optimization, constrained optimization, Lagrange method, Kruskal-Kuhn-Tucker method

Preparation
Please study the following Handout 3.

Exercises
Please solve the following problems and hand in your solutions of the marked questions by 25.09.2023 at the latest.

Timetable
Tue, 12.09.23, 09:15-12:00 (Seminarraum S5, Juristische Fakultät)
1. Part Theoretical foundations (presentation of the handout): local and global extremal points, unconstrained optimization, constrained optimization, Lagrange method

2. Part Self-study (of the handout), questions and work on the exercises
Wed, 13.09.23, 09:15-12:00 (Seminarraum S5, Juristische Fakultät)
1. Part Theoretical foundations (presentation of the handout): Kruskal-Kuhn-Tucker method
2. Part Self-study (of the handout), questions and work on the exercises

Thu, 14.09.23, 09:15-12:00 (Seminarraum S5, Juristische Fakultät)
Only Self-study (of the handout), questions and work on the exercises