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Mathematics Dynamic Analysis ( forår 2008 - 5 ECTS )

Rammer for udbud

  • Uddannelsessprog: (se under Undervisnings- og arbejdsform)
  • Niveau: Elective course in the 4 th semester of the BSc Economics and Management program
  • Semester/kvarter: Each spring
  • Timer per uge: 4 lectures + 2 tutorials for 7 weeks
  • Deltagerbegrænsning: None
  • Undervisningssted: Århus
  • Hovedområde: Det Samfundsvidenskabelige Fakultet
  • Udbud ID: 10912

Formål

The objectives are that the student after having participated in this course should be able to

·         formulate and interpret dynamic economic and mathematical statements precisely by help of mathematical terminology and symbols

·         formulate, interpret and solve first- and higher-order linear differential equations and difference equations

·         formulate, interpret and in simple cases solve first- and second-order non-linear differential equations and difference equations

·         apply, explain and interpret phase diagrams to ascertain the qualitative properties of the time path for the dynamic solution process of non-linear differential equations and difference equations

·         apply and interpret complex numbers and their basic properties and alternative representations

·         apply and interpret the basic circular functions and their basic properties

·         solve simultaneous linear differential equations and difference equations with constant coefficients

·         apply, explain and interpret two variable phase diagrams to ascertain the qualitative properties of the time path for the dynamic solution processes of non-linear differential equations

·         linearize non-linear differential equations system and perform and explain a local stability analysis on the resulting system

·         formulate optimal control problems, apply the maximum principle to find solutions and analyze and interpret these

·         apply the above mentioned mathematical tools on economic problems in order to find results, that can be applied and analyzed within an economic context

 

Indhold

When we analyse the economic development over time, we need to have available the mathematical tools to handle dynamic models. This course introduces difference and differential equations as well as complex numbers and circular functions, which are obvious tools to use, when analysing the dynamic path of an economy. In order to be able to understand how to dose the economic means in the right way to control the development of the economy over time the course will also give an introduction to dynamic optimization. Economic applications will be emphasized throughout the course, and the introduction of a mathematical software program to solve dynamic problems will be an integral part of the teaching.

 

 

COURSE SUBJECT AREAS:

1.       Complex numbers and circular functions

2.       First- and higher-order differential equations

3.       First- and higher-order difference equations

4.       Simultaneous differential equations and difference equations

5.       Optimal control theory

Faglige forudsætninger

(Progression):

Macroeconomics, Mathematics and Statistics (2 nd semester course) and Microeconomics, Mathematics and Statistics (3 rd semester course).

 

Underviser

Michael H.J. Stæhr

Undervisnings- og arbejdsform

Lectures and tutorials

Danish

Litteratur

1.      Alpha C. Chiang and Kevin Wainwright: Fundamental Methods of Mathematical Economics. Fourth edition. Boston : McGraw-Hill Irwin, 2005. C h. 15-20. (180 pages)

2.       Miroslaw Majewski: Getting Started with MuPAD. Berlin : Springer-Verlag, 2005. (This is an introduction to the Math program and should be considered as supplementary reading)

 

Notes, weekly exercises and assignments are part of the curriculum.

 

Studieordning og bedømmelse


Bacheloruddannelsen i økonomi

  • Mundtlig, bedømt efter 7-skala med intern censur


Individual oral exam of 20 minutes duration

 

EXAMINATION AIDS ALLOWED: None