Advanced Mathematics for Economics (HS22)

• 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 must) be solved. If you hand in the solutions 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.

When?: 25.10.2022, 17:00-18:30
Where?: Seminarraum S14 (WWZ)

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

Allowed non-electronic means:
open-book

Keywords
vector, matrix, eigenvalue, eigenvector, diagonalization, linear transformation, vector space
Preparation
Please study the following Handout 1.
Exercises
Please solve the following problems and hand in your solutions of the marked questions by 26.09.22 at the latest.

Timetable

• Mo, 05.09.22, 09:15-12:00 (Seminarraum S15, WWZ): Theoretical foundations (presentation of the handout and examples)
• Tue, 06.09.22, 09:15-12:00 (Seminarraum S15, WWZ): Self-study (of the handout), questions and work on the exercises
• We, 07.09.22, 09:15-12:00 (Seminarraum S15, WWZ): Self-study (of the handout), questions and work on the exercises

Keywords
partial derivative, gradient, Hesse matrix, differential, directional derivative, chain rule, implicit function and derivative, Taylor formula, unconstrained optimization
Preparation
Please study the following Handout 2.
Exercises
Please solve the following problems and hand in your solutions of the marked questions by 26.09.22 at the latest.

Timetable

• Thu, 08.09.22, 09:15-12:00 (Seminarraum S14, WWZ): Theoretical foundations (presentation of the handout and examples)
• Fri, 09.09.22, 09:15-12:00 (Seminarraum S14, WWZ): Self-study (of the handout), questions and work on the exercises
• Mo, 12.09.22, 09:15-12:00 (Seminarraum S14, WWZ): Self-study  (of the handout), questions and work on the exercises

Keywords
local and global extremal points, unconstrained optimization, constrained optimization, Lagrange method, 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 26.09.22 at the latest.

Timetable

• Tue, 13.09.22, 09:15-12:00 (Seminarraum S14, WWZ): Theoretical foundations (presentation of the handout and examples)
• Wed, 14.09.22, 09:15-12:00 (Seminarraum S14, WWZ): Self-study  (of the handout), questions and work on the exercises
• Thu, 15.09.22, 09:15-12:00 (Seminarraum S14, WWZ): Self-study  (of the handout), questions and work on the exercises