Numerical Algorithms in Computer Science, 4 credits (TANA09)
Datatekniska beräkningar, 4 hp
Main field of study
Mathematics Applied MathematicsLevel
First cycleCourse type
Programme courseExaminer
Fredrik BerntssonDirector of studies or equivalent
Ingegerd SkoglundCourse offered for | Semester | Period | Timetable module | Language | Campus | VOF | |
---|---|---|---|---|---|---|---|
6CDDD | Computer Science and Engineering, M Sc in Engineering | 7 (Autumn 2017) | 2 | 1 | Swedish | Linköping | o/v |
6CITE | Information Technology, M Sc in Engineering | 7 (Autumn 2017) | 2 | 1 | Swedish | Linköping | o/v |
6CMJU | Computer Science and Software Engineering, M Sc in Engineering | 7 (Autumn 2017) | 2 | 1 | Swedish | Linköping | v |
6CDDD | Computer Science and Engineering, M Sc in Engineering | 9 (Autumn 2017) | 2 | 1 | Swedish | Linköping | o/v |
6CITE | Information Technology, M Sc in Engineering | 9 (Autumn 2017) | 2 | 1 | Swedish | Linköping | o/v |
Main field of study
Mathematics, Applied MathematicsCourse level
First cycleAdvancement level
G2XCourse offered for
- Computer Science and Engineering, M Sc in Engineering
- Information Technology, M Sc in Engineering
- Computer Science and Software Engineering, M Sc in Engineering
Entry requirements
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.
Prerequisites
Basic courses in calculus, linear algebra and programming.Intended learning outcomes
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.
Course content
- 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.
Teaching and working methods
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.
Examination
TEN1 | Written examination | U, 3, 4, 5 | 2.5 credits |
LAB1 | Computer assignments, compulsory attendance at sessions | U, G | 1.5 credits |
Grades
Four-grade scale, LiU, U, 3, 4, 5Other information
Supplementary courses: Numerisk linjär algebra, Numerisk linjär analys
Department
Matematiska institutionenDirector of Studies or equivalent
Ingegerd SkoglundExaminer
Fredrik BerntssonCourse website and other links
http://courses.mai.liu.se/GU/TANA09Education components
Preliminary scheduled hours: 38 hRecommended self-study hours: 69 h
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.
TEN1 | Written examination | U, 3, 4, 5 | 2.5 credits |
LAB1 | Computer assignments, compulsory attendance at sessions | U, G | 1.5 credits |
Regulations (apply to LiU in its entirety)
The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.
LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.
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