DAVE3705 Mathematics 4000 Course description

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.

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.

No requirements over and above the admission requirements.

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
• 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
• 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

Ordinary differential equations with variable coefficients

Laplace transforms

Fourier series

Partial differential equations

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.

The following coursework is compulsory and must be approved before the student can sit the exam:

• 1 individual written assignment

Individual written exam, 3 hours.

The exam result can be appealed.

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.

Grade scale A-F.

One internal examiner. External examiners are used regularly.

Sergiy Denysov