Entry requirements

120 credits including at least 60 credits in mathematics. Proficiency in English equivalent to the Swedish upper secondary course English 6.

Learning outcomes

The course aims at giving an introduction to the exciting borderland between mathematics and applied areas of heavy computations by presenting a number of important methods and techniques in applied mathematics.

On completion of the course, the student should be able to:

• give examples of a number of important such methods and techniques, and describe some main types of applied problems where these methods can be used;
• formulate applied problems that are susceptible to using the techniques presented during the course mathematically in such a way that the techniques are applicable;
• solve standard problems within the areas covered by the course.

Content

The course gives an introduction to a number of modern methods and techniques in applied mathematics via examples from applied areas. It consists of the following rather independent items: dimension analysis and scaling, perturbation methods, calculus of variation, elementary partial differential equations, Sturm-Liouville theory and associated theory for generalised Fourier series and Fourier's method, theory of transforms, Hamiltonian theory and isoperimetric problems, integral equations, dynamical systems (chaos, stability and bifurcations), discrete mathematics, and briefly about some other useful techniques in applied mathematics (distribution theory, similarity methods, homogenisation, etc.)

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course combined with assignments given during the course.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.