Advanced Mathematics for Economists

The course provides the students with the basic mathematical skills necessary to understand central analytical methods in economic theory. The main part of the course covers mathematical analysis with multivariable functions, with applications for theories of consumption and production. In addition, the course consists of integration, differential equations and linear algebra.

Knowledge

You learn

• about definite and indefinite integrals of one variable and several variables, techniques for solving integrals (integration by parts and integration by substitution)
• how geometric series can be used in financial mathematics
• linear algebra, including addition and multiplication of vectors and matrices, geometric interpretation of vectors, solution of linear systems of equations, linear independence, rank of matrices, determinants, eigenvalues and eigenvectors
• about first-and second-order differential equations, phase plane analysis and directional diagrams, systems of differential equations, saddle points, simple difference equations
• about optimization of functions defined over multiple variables with and without constraints, how to determine whether extreme points are minimum, maximum or saddle points
• about production technology, cost minimization and cost function, profit maximization and profit function, utility functions and consumer theory

Skills

You should be able to

• determine fairly complicated integrals
• calculate present values and find the annuity for an annuity loan
• use linear algebra to solve linear systems of equations, compute determinants, find the rank of matrices and find the eigenvalues and associated eigenvectors
• solve and analyze first-and second-order differential equations, including systems of differential equations
• find optimum for static optimization problems, and apply optimization on microeconomic issues

General competence

You should be able to

• use mathematics as a tool to analyze economic issues
• apply mathematics in quantitatively oriented courses, such as macroeconomics, econometrics and finance

4 hours of lectures every week. Information about tutorials and compulsory activity will be announced at the beginning of the term.