Advanced Mathematics for Economics


Content

  • In the first part of this course we will give a review of linear algebra, functions and Taylor's formula.
  • In the second part we study optimization problems (unconstrained and constrained).
  • In the third part of this course we will study (ordinary) differential equations and systems of differential equaitions.

Complementary literature

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.

Organsational Matters

No general lessons
Please study the topics in the handouts (independent/privat study). Start now! You can arrange (no more than three a head) individual question times (via Zoom) for discussions and questions.

Performance review
Exercises must be solved and you should hand in the solutions. 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.

Examination

When? Saturday, 06 November 2021, 14:30-16:00
Where? Seminarraum S15 (WWZ, Hofgeschoss)

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

Allowed non-electronic means:
open-book


Course Arc

1. Part: Linear algebra, vector spaces, functions and Taylor's formula

Please solve the following problems and submit your solutions of the marked questions by  24 September 2021 at the latest.

Linear algebra and vector spaces

Keywords
vector, matrix, eigenvalue, eigenvector, diagonalization, linear transformation, vector space
Preparation
Please study the following Handout 1.
Zoom-Meeting
Problems and questions? Make an appointment

Functions and Taylor's formula

Keywords
partial derivative, gradient, Hesse matrix, differential, directional derivative, chain rule, implicit function and derivative, Taylor formula, unconstrained optimization 
Preparation
Please read (and study) the following Handout 2.
Zoom-Meeting
Problems and questions? Make an appointment

2. Part: Static optimization

Please solve the following problems and submit your solutions of the marked questions by 24 September 2021 at the latest.

Keywords
local and global extremal points, unconstrained optimization, constrained optimization, Lagrange method, Kuhn-Tucker method
Preparation
Please read and study the following Handout 3.
Zoom-Meeting
Problems and questions? Make an appointment

3. Part: Differential equations

Please solve the following problems and submit your solutions of the marked questions by  24 September 2021 at the latest..

Keywords
differentiable processes, differential equations, systems of differential equations, linear systems with constant coefficients
Preparation
Please read and study the following Handout 4.
Zoom-Meeting
Problems and questions? Make an appointment