Difference and Differential Equations

MAT11 Difference and Differential Equations

Autumn 2020

  • 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

    ii) PC lab: once 2x45

  • 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.

Overview

ECTS Credits
7.5
Teaching language
Norwegian
Semester

Autumn. Offered Autumn 2020.

Written school exam is offered both semesters (according to Regulations for Full-time Study Programmes at the Norwegian School of Economics (NHH), section 3-1).

Please note: Due to the present corona situation, please expect parts of this course description to be changed before the autumn semester starts. Particularly, but not exclusively, this relates to teaching methods, mandatory requirements and assessment.

Course responsible

Professor Roman Kozlov, Department of Business and Management Science.