| TANA21 |
Scientific Computing , 6 ECTS credits.
/Beräkningsmatematik/
For:
D
FyN
I
Ii
IT
M
MED
U
Y
Yi
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Prel. scheduled
hours: 52
Rec. self-study hours: 108
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G1
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Aim:
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
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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.
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Supplementary courses:
Numerical linear algebra, Numerical linear calculus
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Organisation:
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.
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Course contents:
- 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.
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Course literature:
L Eldén, L Wittmeyer-Koch: Numeriska beräkningar - analys och illustrationer med MATLAB, fjärde upplagan, Studentlitteratur, 2001.
H Brandén, �-vningar i Beräkningsmatematik, MAI, LiU.
H Brandén, Formelsamling i Beräkningsmatematik, MAI, LiU.
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Examination: |
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Written examination
Laboratory work
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4 ECTS
2 ECTS
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The first three 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: Ingegerd Skoglund
Link to the course homepage at the department
Course Syllabus in Swedish
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