Videregående matematikk og optimering

The course will make students better suited to meeting the demands in mathematics, which they will face in other upper-bachelor and master-level economics courses.

The course deals with linear algebra, the functions of several variables, comparative statistics and optimization with several variables and restrictions. In optimization, the Lagrange and Kuhn-Tucker methods are the main points of focus.

A student who has completed the course should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student can ...

• comprehend the following conversions and concepts within linear algebra: Addition, subtraction and scalar multiplication of vectors, vector length, distance between vectors and inner product between vectors, lines and planes, hyperplanes in parametric and non-parametric representation, linear independence.
• give a description of: square shapes, positive and negative semidefinite matrices, convex amounts and functions.
• distinguish constraint and no constrain optimization problems as well as dynamic and non-dynamic optimization problems.
• reflect on the necessary conditions for global or local maxima‘s and minima‘s.
• discuss the application of the envelope theory for optimization problems in economics.

Skills 

The student can ...

• apply addition and multiplication of matrices, the identity matrix, inverse matrix and linear equation system on matrix form. The student should be able to determine the rank of an array to classify linear equation systems. They should also be able to calculate determinants and be able to use Cramer's rules for linear equations.
• apply partial derivative, total differential, gradient vector and directional derivative as well as implicit derivation, second order partial derivative and hesseian matrix. The student should be able to use comparative statistics on an equation system.
• apply Lagrange and Kuhn-Tucker methods for solving optimization problems with restrictions.