Scientific Computing, 6 credits (TANA21)

Beräkningsmatematik, 6 hp

Main field of study

Mathematics Applied Mathematics

Level

First cycle

Course type

Programme course

Examiner

Ingegerd Skoglund

Director of studies or equivalent

Ingegerd Skoglund
Course offered for Semester Period Timetable module Language Campus VOF
6KFYN Physics and Nanotechnology 5 (Autumn 2017) 1 3 Swedish Linköping v
6CDDD Computer Science and Engineering, M Sc in Engineering 7 (Autumn 2017) 1 3 Swedish Linköping o/v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - French 7 (Autumn 2017) 1 3 Swedish Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - French (Specialization Mechanical Engineering) 7 (Autumn 2017) 1 3 Swedish Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Japanese 7 (Autumn 2017) 1 3 Swedish Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Japanese (Specialization Mechanical Engineering) 7 (Autumn 2017) 1 3 Swedish Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Spanish 7 (Autumn 2017) 1 3 Swedish Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Spanish (Specialization Mechanical Engineering) 7 (Autumn 2017) 1 3 Swedish Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - German 7 (Autumn 2017) 1 3 Swedish Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - German (Specialization Mechanical Engineering) 7 (Autumn 2017) 1 3 Swedish Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Chinese 7 (Autumn 2017) 1 3 Swedish Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Chinese (Specialization Mechanical Engineering) 7 (Autumn 2017) 1 3 Swedish Linköping v
6CIII Industrial Engineering and Management, M Sc in Engineering 7 (Autumn 2017) 1 3 Swedish Linköping v
6CIII Industrial Engineering and Management, M Sc in Engineering (Specialization Mechanical Engineering) 7 (Autumn 2017) 1 3 Swedish Linköping v
6CITE Information Technology, M Sc in Engineering 7 (Autumn 2017) 1 3 Swedish Linköping o/v
6CMED Biomedical Engineering, M Sc in Engineering 7 (Autumn 2017) 1 3 Swedish Linköping v
6CMED Biomedical Engineering, M Sc in Engineering (Biomedical Imaging and Visualization) 7 (Autumn 2017) 1 3 Swedish Linköping v
6CMJU Computer Science and Software Engineering, M Sc in Engineering 7 (Autumn 2017) 1 3 Swedish Linköping v
6CMMM Mechanical Engineering, M Sc in Engineering 7 (Autumn 2017) 1 3 Swedish Linköping v
6CDDD Computer Science and Engineering, M Sc in Engineering 9 (Autumn 2017) 1 3 Swedish Linköping o/v
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering 3 (Autumn 2017) 1 3 Swedish Linköping o
6CITE Information Technology, M Sc in Engineering 9 (Autumn 2017) 1 3 Swedish Linköping o/v
6CTBI Engineering Biology, M Sc in Engineering (Devices and Materials in Biomedicine) 7 (Autumn 2017) 1 3 Swedish Linköping o/v
6CTBI Engineering Biology, M Sc in Engineering (Industrial biotechnology and production) 7 (Autumn 2017) 1 3 Swedish Linköping o/v
6CKEB Chemical Biology, M Sc in Engineering (Industrial Biotechnology and Production) 7 (Autumn 2017) 1 3 Swedish Linköping o/v
6CKEB Chemical Biology, M Sc in Engineering (Protein Science and Technology) 7 (Autumn 2017) 1 3 Swedish Linköping o/v

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Physics and Nanotechnology
  • Computer Science and Engineering, M Sc in Engineering
  • Industrial Engineering and Management - International, M Sc in Engineering
  • Industrial Engineering and Management, M Sc in Engineering
  • Information Technology, M Sc in Engineering
  • Biomedical Engineering, M Sc in Engineering
  • Computer Science and Software Engineering, M Sc in Engineering
  • Mechanical Engineering, M Sc in Engineering
  • Applied Physics and Electrical Engineering, M Sc in Engineering
  • Engineering Biology, M Sc in Engineering
  • Chemical Biology, 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

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 computationl 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, where acquired knowledge and skills are used.

Examination

TEN1Written examinationU, 3, 4, 54 credits
LAB1Laboratory workU, G2 credits
The first three 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: 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/TANA21

Education components

Preliminary scheduled hours: 52 h
Recommended self-study hours: 108 h

Course literature

Additional literature

Books
L Eldén, L Wittmeyer-Koch, (2001) Numeriska beräkningar - analys och illustrationer med MATLAB fjärde upplagan Studentlitteratur
Compendiums
H Brandén, Formelsamling i Beräkningsmatematik, MAI, LiUH Brandén, Övningar i Beräkningsmatematik, MAI, LiU

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
TEN1 Written examination U, 3, 4, 5 4 credits
LAB1 Laboratory work U, G 2 credits
The first three 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. 

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