Difference and Differential Equations

MAT11 Difference and Differential Equations

Autumn 2024

Spring 2024
  • 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 differential equations. 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 (pen and paper).

    An assessment will not be organised in the the non-teaching semester (spring).

  • 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

    Calculator

    One bilingual dictionary (Category I)

    Formula collection (Category II): 

    Matematisk formelsamling for økonomer - by Knut Sydsæter, Arne Strøm, Peter Berck, Oslo, Gyldendal akademisk, 2006 (4th edition. Previous editions can also be used).

    All in accordance with Supplementary provisions to the Regulations for Full-time Study Programmes at the Norwegian School of Economics Ch.4 Permitted support material https://www.nhh.no/en/for-students/regulations/https://www.nhh.no/en/for-students/regulations/ and https://www.nhh.no/en/for-students/examinations/examination-support-materials/https://www.nhh.no/en/for-students/examinations/examination-support-materials/ 

Overview

ECTS Credits
7.5
Teaching language
Norwegian
Semester

Autumn. Offered autumn 2024

Course responsible

Professor Roman Kozlov, Department of Business and Management Science.