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. 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.
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.)
Lectures and problem solving sessions.
Written examination at the end of the course combined with assignments given during the course.