AU kursuskatalog arkiv

2635: Mathematics - Dynamic Analysis ( forår 2011 - 5 ECTS )

Rammer for udbud

• Uddannelsessprog: dansk
• Niveau: Elective course in the 4 th semester of the BSc Economics and Management program
• Semester/kvarter: Every spring semester
• Timer per uge: 4 lectures for 7 weeks + 2 extra lectures + 4 times 3 hours of tutorials
• Deltagerbegrænsning: None
• Undervisningssted: Århus
• Hovedområde: Det Samfundsvidenskabelige Fakultet
• Udbud ID: 26433

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
• explain and apply eigenvalues and eigenvectors 
• 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 apply 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 eigenvalues and -vectors, 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. Eigenvalues and -vectors 
3. First- and higher-order differential equations
4. First- and higher-order difference equations
5. Simultaneous differential equations and difference equations
6. Optimal control theory

Faglige forudsætninger

The compulsory courses in the first three semesters of the BSc. Economics and Management programme, and the course "Growth and International Trade". 

Underviser

Anne Floor Sørensen, Peter Bache Arendorf

Undervisnings- og arbejdsform

Lectures and tutorials

Litteratur

Carl P. Simon and Lawrence Blume: Mathematics for Economists. New York: W.W. Norton & Company, 1994. Ch.23. Knut Sydsæter, Peter Hammond, Atle Seierstad and Arne Strøm, Mathematics - Dynamic Analysis. Harlow, Essex: Pearson Education Limited, 2010.

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