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Valid for year : 2008
 
TANA02 Scientific Computing , 6 ECTS credits.
/Tekniska beräkningar /

For:   Fys   KA   Mat   Y   Yi  

 

Prel. scheduled hours: 52
Rec. self-study hours: 108

  Area of Education: Science

Subject area: Mathematics
  Advancement level (G1, G2, A): G1

Aim:
Within the area of scientific computing algorithms for solution of mathematical problems in science and technology are developed. The student should aquire knowledge of basic concepts within the field, and gain familarity with certain numerical algorithms. After this course the student should be able to
  • use and to some extent analyse common numerical methods for solving linear/nonlinear equations and ordinary differential equations
  • use methods for numerical differentiation
  • analyse the influence of errors in computed results
  • use methods for curvefitting to given data sets
  • write simple Matlab programs and also be able to use built in Matlab routines for solving more complex problems


Prerequisites: (valid for students admitted to programmes within which the course is offered)
Calculus, linear algebra, basic programming course

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
Supplementary courses:
Fortran, Numerical methods II, Numerical solution of partial differential equations, Programming of parallel computers and Scientific Computing
Organisation:
The theory is presented in the lectures. The exercises exemplify the theory. The computer exercises investigate numerical properties of algorithms and software.
Course contents:
Error analysis: Error propagation, floating point numbers. Solution of a nonlinear equation: Bisection, Newton-Raphson's method, iteration theory. Curve fitting: Interpolation by polynomials and splines. Linear algebra: Gaussian elimination, LU-factorization, pivoting, perturbation analysis, least squares method. Numerical differentiation, Richardson extrapolation. Initial value problems: Runge-Kutta methods, implicit methods, stability. Boundary value problems: The finite elementmethod.
Course literature:
Eldén, Wittmeyer-Koch: Numeriska beräkningar- analys och illustrationer med Matlab. Studentlitteratur. The English edition: Eldén, Wittmeyer-Koch: Numerical Analysis an Introduction. Department of Mathematics, 1995. Elfving, Eriksson, Ouchterlony, Skoglund: Numeriska beräkningar - en exempelsamling. Studentlitteratur. From the department: Instructions for the computer exercises.
Examination:
Written examination
Laboratory work
 4 ECTS
2 ECTS
 


Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Tommy Elfving
Examiner: Tommy Elfving
Link to the course homepage at the department


Course Syllabus in Swedish

Linköping Institute of Technology
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Contact: TFK , val@tfk.liu.se
Last updated: 06/11/2015