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.