Type of course

Admission requirements

Course content

The objective of the course is to introduce some of the basic notions and methods in the mathematics of modelling, numerical analysis, and optimization. These subjects have shown to be important in applied mathematics.

The main topic of the course is some methods that are used scientific computing, for example the Newton, Ritz, Galerkin, and least squares methods, polynomial approximations in Sobolev spaces, the Fourier transform, and spectral methods. Construction of numerical methods for optimization, algebraic equations, and for classical PDEs associated to wave, heat, and fluid dynamics. Methods based on rigorous numerics using interval analysis.

Objectives of the course

Knowledge:
After passing the course, the student is expected to be able to

• Give an account of basic concepts and definitions in the mathematics of modelling, numerical analysis, and optimization.
• Formulate results covered by the course.
• Exemplify concepts in specific cases.

Skills:
After passing the course, the student is expected to be able to

• Interpret concepts in specific cases.
• Describe the main features of the proofs of main theorems.

Habits of mind:
After passing the course, the student is expected to be able to

• Use the theory and methods of the course to solve problems in applied mathematics.

Language of instruction and examination

Teaching methods

Assessment

Oral exam: Passed/Not passed.

A re-sit exam will be arranged for this course.

Recommended reading/syllabus

Material will be selected from several sources, including

• Warwick Tucker. Validated Numerics: A Short Introduction to Rigorous Computations. Princeton University Press, 2011.
• Allaire, Grégoire. Numerical analysis and optimization: an introduction to mathematical modelling and numerical simulation. Oxford University Press, 2007.
• Bertil Gustavsson: Fundamentals of Scientific Computing, Springer Verlag 2011.