EPN-V2

DAVE3705 Mathematics 4000 Course description

Course name in Norwegian
Matematikk 4000
Weight
10.0 ECTS
Year of study
2024/2025
Course history
Curriculum
SPRING 2025
Schedule
Programme description

  • Introduction

    The course shall prepare students for master’s degree programmes at universities and university colleges where different types of differential equations is used.

    The elective course is initiated provided that a sufficient number of students choose the course.

  • Recommended preliminary courses

    The course builds on Mathematics 1000 and Mathematics 2000 (all study programs), but is independent of Mathematics 3000 and can therefore be taken in the 4th semester if the rest of the study portfolio allows for this.

  • Required preliminary courses

    No requirements over and above the admission requirements.

  • Learning outcomes

    After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills and general competence:

    Knowledge

    The student is capable of:

    • explaining the concepts of analytic function, ordinary, singular and regular singular points
    • using series to solve differential equations
    • defining the Laplace transform and derive it's basic properties
    • explaining what characterize Fourier series and how they can be used to solve ordinary and partial differential equations
    • recognizing and understanding concepts of complex functions
    • giving examples of elliptical, parabolic and hyperbolic partial differential equations and how they are solved

    Skills

    The student is capable of:

    • solving higher order linear differential equations with constant coefficients
    • using power series and Frobenius series to solve second order linear differential equations with variable coefficients
    • manipulate functions of complex variables
    • using the Laplace transform to solve non-homogeneous linear differential equations modelling oscillating systems
    • determining the Fourier sine series and the Fourier cosine series of symmetrical expansions of non-periodic functions
    • solving boundary value problems relating to partial differential equations in closed domains by separation of variables

    General competence

    The student:

    • has acquired good skills in solving ordinary and partial differential equations
    • utilizing complex analysis techniques to solve partial differential equations, related to electrical engineering, acoustic and heat transfer

  • Content

    Ordinary differential equations with variable coefficients

    Laplace transforms

    Fourier series

    Partial differential equations

  • Teaching and learning methods

    Lectures and exercises. Practical exercises are solved individually with the help of the pre-written compendium with solutions for all exercises and previous exams. At the end of the course, previous exams will be reviewed during the six weekly periods.

  • Course requirements

    None

  • Assessment

    Individual written exam, 3 hours.

    The exam result can be appealed.

  • Permitted exam materials and equipment

    Aids enclosed with the exam question paper, and a handheld calculator that cannot be used for wireless communication or to perform symbolic calculations. If the calculator’s internal memory can store data, the memory must be deleted before the exam. Random checks may be carried out.

  • Grading scale

    Grade scale A-F.

  • Examiners

    One internal examiner. External examiners are used regularly.

  • Course contact person

    Sergiy Denysov