Entry requirements

120 credits including at least 60 credits Mathematics

Learning outcomes

The course aims at giving an introduction to the borderland between mathematics and its applied areas by presenting a number of important methods and techniques in applied mathematics. In order to pass the course (grade 3) 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. The course consists of five items chosen among the following ten:

• 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.

All ten items cannot be guaranteed every academic year.

Instruction

Lectures and problem solving sessions.

Assessment

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