Numerical Algorithms in Computer Science, 4 credits

Datatekniska beräkningar, 4 hp

TANA09

Course starting semester

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Fredrik Berntsson

Director of studies or equivalent

Ingegerd Skoglund

Education components

Preliminary scheduled hours: 38 h
Recommended self-study hours: 69 h

Possible deviation from course syllabus/programme syllabus

ECV = Elective / Compulsory / Voluntary

Course offered for		Semester	Period	Timetable module	Language	Campus	ECV
6CDDD	Computer Science and Engineering, M Sc in Engineering	7 (Autumn 2017)	2	1	Swedish	Linköping, Valla	C/E
6CDDD	Computer Science and Engineering, M Sc in Engineering	9 (Autumn 2017)	2	1	Swedish	Linköping, Valla	C/E
6CMJU	Computer Science and Software Engineering, M Sc in Engineering	7 (Autumn 2017)	2	1	Swedish	Linköping, Valla	E
6CITE	Information Technology, M Sc in Engineering	7 (Autumn 2017)	2	1	Swedish	Linköping, Valla	C/E
6CITE	Information Technology, M Sc in Engineering	9 (Autumn 2017)	2	1	Swedish	Linköping, Valla	C/E

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G2X

Course 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

LAB1	Computer assignments, compulsory attendance at sessions	1.5 credits	U, G
TEN1	Written examination	2.5 credits	U, 3, 4, 5

The three first course aims are examined with TEN1. The fourth is examined with LAB1.

Grades

Four-grade scale, LiU, U, 3, 4, 5

Other information

Supplementary courses: Numerisk linjär algebra, Numerisk linjär analys

Department

Matematiska institutionen

Director of Studies or equivalent

Ingegerd Skoglund

Examiner

Fredrik Berntsson

Course website and other links

http://courses.mai.liu.se/GU/TANA09

Education components

Preliminary scheduled hours: 38 h
Recommended 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.

Code	Name	Scope	Grading scale
LAB1	Computer assignments, compulsory attendance at sessions	1.5 credits	U, G
TEN1	Written examination	2.5 credits	U, 3, 4, 5

The three first course aims are examined with TEN1. The fourth is examined with LAB1.

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.

Student rights and obligations (login required)
Linköping University common rules and regulations (in Swedish)

Course literature is preliminary.

L Eldén, L Wittmeyer-Koch: Numeriska beräkningar - analys och illustrationer med MATLAB, fjärde upplagan, Studentlitteratur, 2001. <br>Elfving, Eriksson, Ouchterlony, Skoglund: Numeriska beräkningar - en exempelsamling. Studentlitteratur 2002.

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Download course literature list as PDF

Note: The course matrix might contain more information in Swedish.

I = Introduce, U = Teach, A = Utilize

		U	A	Modules
1. DISCIPLINARY KNOWLEDGE AND REASONING
	1.1 Knowledge of underlying mathematics and science (G1X level)	X	X	TEN1
	1.2 Fundamental engineering knowledge (G1X level)		X
	1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)
	1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)
	1.5 Insight into current research and development work
2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
	2.1 Analytical reasoning and problem solving	X	X	LAB1
	2.2 Experimentation, investigation, and knowledge discovery	X	X	LAB1
	2.3 System thinking
	2.4 Attitudes, thought, and learning		X
	2.5 Ethics, equity, and other responsibilities
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
	3.1 Teamwork		X
	3.2 Communications
	3.3 Communication in foreign languages
4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
	4.1 External, societal, and environmental context
	4.2 Enterprise and business context
	4.3 Conceiving, system engineering and management
	4.4 Designing
	4.5 Implementing
	4.6 Operating
5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS
	5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development
	5.2 Economic conditions for knowledge development
	5.3 Identification of needs, structuring and planning of research or development projects
	5.4 Execution of research or development projects
	5.5 Presentation and evaluation of research or development projects

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