Scientific Computing, 8 credits

Beräkningsmatematik, 8 hp

TANA22

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Ingegerd Skoglund

Director of studies or equivalent

Ingegerd Skoglund

Education components

Preliminary scheduled hours: 60 h
Recommended self-study hours: 153 h
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6KMAT Mathematics, Bachelor´s Programme 3 (Autumn 2017) 1 3 Swedish Linköping C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Mathematics, Bachelor´s Programme

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

Computational mathematics is the art of developing and analysing numerical algorithms for solving mathematical problems in for example natural science and technology. After finishing the course the student should be able to

  • explain and separate fundamental terms and concepts in computational mathematics
  • use a selection of numerical algorithms for solving given mathematical problems using a pocket calculator
  • estimate the accuracy of calculated results
  • use mathematical software

Course content

  • Error analysis: Round off, truncation, error propagation and cancellation.
  • Linear systems of equations: LU decomposition, pivoting, backward and forward substitution, condition and arithmetic complexity.
  • Interpolation and approximation: Newton's and Lagrange's methods, splines, Horner's scheme, least squares and overdetermined systems.
  • Differentiation and integration: Difference approximation, order of accuracy, the trapezoidal rule, and Simpon's rule.
  • Ordinary differential equations: Runge Kutta methods, local and global truncation error, stability and convergence.
  • Floting point numbers: Floating point systems, machine epsilon and round off.
  • Non-linear equations: The bisection method, Newton-Raphson's method, fixed point iteration, condition and order of convergence.

Teaching and working methods

The course is divided into a number of sections that are described under Course contents below. Each sections begins with a preparatory computer laboration that gives training in using mathematical software and raises questions about the properties of the numerical algorithms. These questions are answered during lectures, when the algorithms are explained.

The ability to explain and separate terms and concepts in computational mathematics, the ability to use numerical algorithms using a pocket calculator and the ability to estimate the accuracy of calculated results are trained during exercise time.

A number of minor projects are also carried out in group, where acquired knowledge and skills are used, and some exercises i MATLAB.

Examination

UPG1Project work2 creditsU, G
LAB1Laboratory work2 creditsU, G
TEN1Written examination4 creditsU, 3, 4, 5
The first three course aims are examined with TEN1. The fourth is examined with LAB1 and UPG1.

Grades

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

Other information

Supplementary courses: Numerical linear algebra. Numerical linear calculus.

Department

Matematiska institutionen

Director of Studies or equivalent

Ingegerd Skoglund

Examiner

Ingegerd Skoglund

Course website and other links

http://courses.mai.liu.se/GU/TANA22

Education components

Preliminary scheduled hours: 60 h
Recommended self-study hours: 153 h

Course literature

Additional literature

Books

  • L Eldén, L Wittmeyer-Koch, (2001) Numeriska beräkningar - analys och illustrationer med MATLAB fjärde upplagan Studentlitteratur

Compendia

  • H Brandén, Formelsamling i Beräkningsmatematik, MAI, LiU
  • H Brandén, Övningar i Beräkningsmatematik, MAI, LiU
Code Name Scope Grading scale
UPG1 Project work 2 credits U, G
LAB1 Laboratory work 2 credits U, G
TEN1 Written examination 4 credits U, 3, 4, 5
The first three course aims are examined with TEN1. The fourth is examined with LAB1 and UPG1.

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. 

Additional literature

Books

L Eldén, L Wittmeyer-Koch, (2001) Numeriska beräkningar - analys och illustrationer med MATLAB fjärde upplagan Studentlitteratur

Compendia

H Brandén, Formelsamling i Beräkningsmatematik, MAI, LiU
H Brandén, Övningar i Beräkningsmatematik, MAI, LiU

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

I = Introduce, U = Teach, A = Utilize
I U A Modules Comment
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
X
UPG1

                            
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
X

                            
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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