Lecturer: Sorin Pop
The purpose of this course is to provide introductory material in numerical methods. The course is
split into two parts, part A and part B. Part A is meant for trainees of all orientations, whereas
part B is meant for trainees of the T-orientation. In part A basic numerical methods and algorithms
are introduced and the main elementary techniques are discussed. Part B is dedicated to special
techniques for solving ordinary and partial differential equations which apply to problems from
mathematical physics, their modeling and numerical simulation. At the end of the course, the trainee
should be able to find appropriate numerical techniques for certain problems, and be able to make a
choice by analyzing the advantages and disadvantages of the available methods.
The topics covered in part A are:
- Numerical techniques for solving linear systems (direct and iterative methods)
- Numerical techniques for the approximation of eigenvalues and eigenvectors
- Numerical techniques for solving nonlinear equations and systems
- Numerical optimization
- Polynomial interpolation
- Numerical integration
Part B is devoted to specific problems, in particular differential equations. Trainees are
confronted with techniques based upon:
- Orthogonal polynomials and transforms
- Gauss-type interpolation and integration
- Approximation of derivatives
- Numerical solution of ordinary differential equations (one-step and multi-step methods,
Runge-Kutta methods, predictor-corrector methods)
- Boundary value problems (finite difference methods, convection dominated problems, finite
element methods)
- Non-stationary problems (parabolic and hyperbolic equations, conservation laws)
Teaching is organized in weekly sessions of two hours. Students are expected to complete their
knowledge by self-study. Assignments are given every week and have to be handed in the week after.
Every two weeks the students are given a team project. Trainees entering the course are expected
to have basic knowledge of analysis, linear algebra, ordinary and partial differential equations.
|
