MAT11 Difference and Differential Equations

• Topics

  The course provides an introduction to basic analytical concepts and solution procedures. The use of the mathematical software package MAPLE is emphasized. The course is divided into four parts.

  Part 1 deals with basic skills in analyzing and solving differential equations and systems of differential equations.

  Part 2 introduces basic notions and key analytical approaches to study the stability of a particular solution. Local and global Liapunov functions are introduced.

  Part 3 deals with basic skills in analyzing and solving difference equations.

  Part 4 focuses on formulating and solving simple dynamical economic problems by introducing classical optimal control theory in continuous time.

• Learning outcome

  KNOWLEDGE

  Students understand basic notions and key analytical approaches in ordinary differential and difference equations used for applications in economic sciences.

  SKILLS

  After completion of the course, the students can solve

  • some first-order differential equations (namely linear, separable, Bernoulli, and projective);
  • systems of linear first-order differential equations;
  • linear (homogeneous and inhomogeneous) higher order differential equations, also using change of variables;
  • some types of linear, homogeneous and inhomogeneous (first order and higher order) difference equations.

  The students can also

  • perform basic linear and nonlinear stability analysis for autonomous (first order and higher order) differential equations and systems of first-order differential equations,
  • perform stability analysis for autonomous linear difference equations with constant coefficients;
  • investigate existence and uniqueness of solutions of differential equations;
  • formulate and solve simple economic problems by using optimal control theory in continuous time;
  • use the mathematical software package MAPLE.

  GENERAL COMPETENCE

  Students can study economic subjects which use ordinary differential and difference equations.

• Teaching

  Plenary lectures: 2 x (2x45) / week.

• Recommended prerequisites

  The course is partially based on MET1 Mathematics for Economists and MAT10 Analysis and Linear Algebra. It is recommended that the students have passed the exams in these courses.

• Credit reduction due to overlap

  Corresponds to MAT011

• Compulsory Activity

  Two obligatory submissions (a written submission and a multiple choice test in Canvas). These assignments must be accepted in order to get admission to the exam.

• Assessment

  Written school exam, 5 hours.

• Grading Scale

  Grading scale A - F.

• Computer tools

  MAPLE. MAPLE materials are provided on the website of the course.

• Literature

  Compulsory literature:

  i) K. Sydsæter: Matematisk analyse, Volume 2: Chap. 1, 2, 3, 9, and 12;

  ii) Selected notes/overheads available in Canvas.

  Recommended literature:

  none.

• Permitted Support Material

  ALLOWED TOOLS:

  1. CALCULATOR

  2. DICTIONARY: A bilingual dictionary is allowed

  3. FORMULA COLLECTION:

  Title: Matematisk formelsamling for økonomer

  Author: Knut Sydsæter, Arne Strøm, Peter Berck

  Year: 2006

  Printed: Oslo, Gyldendal academic

  Edition: 4th edition. Previous editions can also be used.