MM831: Differential Equations II

See Danish version.

The course cannot be chosen by students, who has either followed og passed MM543, MM547 or MM531.

Students taking the course are expected to:

• Know the concept of a
  function, real and complex numbers, differentiation and integration of
  functions of one and several variables, vector calculus, convergence of
  sequences, Newton’s method.
• Be familiar with: systems of linear
  equations, matrices, determinants,  vector spaces, scalar product and
  orthogonality, linear transformations, eigenvectors and eigenvalues,
  diagonalization, polynomials, random variables, normal distribution
• Have
  knowledge of how to implement algorithms as computer programs and
  compute numerical approximations to mathematical problems that don't
  allow a closed form solution.

As acquired in the courses MM536 (Calculus for Mathematics), MM533 (Mathematical and Numerical Analysis), MM538 (Algebra and Linear Algebra), MM507 (Differential equations) / first half of MM545 (Differential equations and geometry).

The learning objectives of the course are that the student demonstrates the ability to:

1. Construct, implement and analyse advanced numerical methods to compute (approximate) solutions to differential equations.
2. Give an oral presentation on an advanced topic and answer supplementary questions on the course syllabus.

The following main topics are contained in the course:

1. Numerical methods: (embedded) Runge-Kutta methods and adaptivity.
2. Stiffness, implicit methods, A-stability.
3. Introduction to Ito-SDEs: Ito integral, Ito process, Ito formula.

Planned lessons

Total number of planned lessons: 42

Hereof:

Common lessons in classroom/auditorium: 42

Classical lectures where the lecturer explains the main parts of the teaching material to the students. This process is carried out while paying particular attention to the active participation of the students.

The lectures are supplied by exercise sessions under the supervision of a teaching assistant. In these sessions, the students are supposed to work with and present exercises related to the material covered in the lectures.


Other planned teaching activities: 

* Reading and understanding of textbook material as preparation for the lectures, either individually or in study groups.

* Preparation of exercises ahead of the exercise sessions, either individually or in study groups.

* Preparation of mandatory assignments.