Applied Mathematics

10 credits

Syllabus, Master's level, 1MA060

This course has been discontinued.

A revised version of the syllabus is available.

Code: 1MA060
Education cycle: Second cycle
Main field(s) of study and in-depth level: Mathematics A1N
Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by: The Faculty Board of Science and Technology, 15 March 2007
Responsible department: Department of Mathematics

Entry requirements

BSc, 60 credit points Mathematics

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.

In order to pass the course (grade 3) the student should be able to

give an account of important concepts and definitions in the area of the course;

exemplify and interpret important concepts in specific cases;

formulate important results and theorems covered by the course;

describe the main features of the proofs of important theorems;

express problems from relevant areas of applications in a mathematical form suitable for further analysis;

use the theory, methods and techniques of the course to solve mathematical problems;

present mathematical arguments to others.

Higher grades, 4 or 5, require a higher level of proficiency. The student should be able to solve problems of greater complexity, i.e. problems requiring a combination of ideas and methods for their solution, and be able to give a more detailed account of the proofs of important theorems and by examples and counter-examples be able to motivate the scope of various results. Requirements concerning the student's ability to present mathematical arguments and reasoning are greater.

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 and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.