MAT11 Difference and Differential Equations

• Topics

  The course provides an introduction to the 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 mathematical software package, MAPLE.

   

  GENERAL COMPETENCE

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

• Teaching

  i) Plenary lectures: 2x (2x45) / week   (with video recording)

  ii) PC lab: once 2x45

  It will be possible to follow the course digitally.

• 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.

• Required prerequisites

  No special requirements

• Credit reduction due to overlap

  Corresponds to MAT011

• Requirements for course approval

  Course approval is given on the basis of two obligatory submissions (a written submission and a multiple choice test in Canvas). These assignments must be accepted in order to get admission for the exam.

• Assessment

  Written school exam, 5 hours.

• Grading Scale

  Grading scale A - F.

• Computer tools

  MAPLE. The syllabus is covered by MAPLE materials 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 special.