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Valid for year : 2007
 
TANA39 Numerical Methods, 6 ECTS credits.
/Numeriska metoder/

For:   ENG   M  

 

Prel. scheduled hours: 60
Rec. self-study hours: 100

  Area of Education: Science

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

Aim:
The aim of the course is to give the students basic knowledge about numerical methods for solving mathematical problems, with applications in science and technology. This includes familarity with terminology and construction of simple numerical methods. The students shall also be able to use numerical algorithms to solve simple problems and to use programs in MATLAB to solve practical problems.
They shall also develop their ability in analysing algorithms and results.

Prerequisites: (valid for students admitted to programmes within which the course is offered)
Basic courses in Calculus, Linear Algebra and Programming.

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:
TANA 70 Fortran. TANA 25 Numerical Methods II. TANA 77 Programming of Parallel Computers, scientific computations.
Organisation:
The course consists of lectures, lessons and computer exercises. The theory is mainly presented at the lectures. Practical examples will be used to illustrate the theory. The lessons emphasize problem solving with calculators and the purpose is to make the students familiar with the methods and their properties. In the computer exercises MATLAB is used to solve numerical problems. Methods and results are analysed and evaluated. Technical applications are used in some examples.
Course contents:
  • Error Analysis: Error Propagation, Cancellation and Rounding Errors in Floating Point Arithmetic.
  • Non-linear Equations: The Bisection Method, Newton-Raphson's Method and the Secant Method. Error Estimation and Theory of Fixed Point Iteration.
  • Interpolation: Newton's Interpolating Polynomial and Spline Interpolation.
  • Numerical Differentiation: Difference Approximation of Derivatives. -Richardson Extrapolation.
  • Numerical Integration: The Trapezoidal Rule and Romberg's Method. Generalized Integrals.
  • Linear Algebra: Gaussian Elimination, LU-Decomposition, Perturbation Theory and Overdetermined Linear Systems (the Least Squares Method). Initial Value Problems: Euler's Method and Runge-Kutta's classical Method. Stability.
  • Boundary Value Problems: The Finite Difference Method.


Course literature:
Lars Eldén, Linde Wittmeyer-Koch: Numeriska beräkningar - analys och illustrationer med Matlab. Studentlitteratur, 2001.
The English edition: Lars Eldén, Linde Wittmeyer-Koch, Hans Bruun Nielsen: Introduction to Numerical Computation - analysis and MATLAB illustrations. Studentlitteratur 2004.
Tommy Elfving, Jan Eriksson, Ulla Ouchterlony, Ingegerd Skoglund: Numeriska beräkningar - en exempelsamling. Studentlitteratur, 2002.
Lars Eldén, Linde Wittmeyer-Koch, Ingegerd Skoglund: FORMELSAMLING till Numeriska beräkningar - analys och illustrationer med Matlab.
From the department: Instructions for the computer exercises.
Examination:
Written examination
Computer exercises
 3 p
1 p
/
/
4 ECTS
2 ECTS
 


Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Tommy Elfving
Examiner: Ulla Ouchterlony
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: 10/09/2007