| TANA09 |
Numerical Algorithms in Computer Science, 4 ECTS credits.
/Datatekniska beräkningar/
For:
D
IT
U
|
| |
Prel. scheduled
hours: 38
Rec. self-study hours: 69
|
| |
Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
|
| |
Advancement level
(G1, G2, A): G2
|
|
Aim:
In the field Computational mathematics numerical methods, for
solving commonly occuring mathematical problems from
applications, are developed and analyzed. Important aspects of
the methods are robustness, accuracy, and efficiency. Since the
methods are intended to be implemented on computers it is
also important to know how a computer treats numerical data.
After having completed the course the student should be able to:
- explain basic concepts from computational mathematics and also
know how a computer stores real numbers and the precision with which
different arithmetic operations can be carried out.
- use a selection of numerical methods for solving mathematical
problems from applications using a pocket calculator or a computer.
- discuss potential sources of errors in numerical calculations and
estimate the accuracy in the computed results.
- use standard mathematical software for solving practical problems from
applications.
|
|
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:
Numerical linear algebra, Numerical linear calculus
|
|
Organisation:
The course consists of lectures, exercises, and computer exercises.
The theory is presented during the lectures. The numerical algorithms
are introduced and analyzed. During the exercises the numerical algorithms
are used to solve problems, and estimate the accuracy of the results,
using a pocket calculator. During the computer exercises more
realistic problems from applications are solved using standard
mathematical software.
|
|
Course contents:
- Error analysis and number representation: The IEE standard for floating point numbers in computers. The machine precision.
Analysis of computational errors. Cancellation. Error propagation and sources of error.
- Linear Algebra: Linear systems of equations. The LU Decomposition. The condition number and error estimate. Least squares problems.
The normal equations. Orthogonal bases. Projections. The QR decomposition.
- Non-linear equations: Bisection. Fixed point iteration. Rate of convergence. Newton-Raphson's method. Error estimate.
- Interpolation: Polynomial- and Splineinterpolation. B-splines. Representation of curves and surfaces in computer graphics
using Bezier polynomials.
|
|
Course literature:
L Eldén, L Wittmeyer-Koch: Numeriska beräkningar - analys och illustrationer med MATLAB, fjärde upplagan, Studentlitteratur, 2001.
Elfving, Eriksson, Ouchterlony, Skoglund: Numeriska beräkningar - en exempelsamling. Studentlitteratur 2002.
|
|
Examination: |
|
Written examination
Computer assignments. Compulsory attendance at sessions.
|
2,5 ECTS
1,5 ECTS
|
| |
|
The three first course aims are examined with TEN1. The fourth is examined with LAB1. |
Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Ingegerd Skoglund
Examiner: Fredrik Berntsson
Link to the course homepage at the department
Course Syllabus in Swedish
|