| TANA19 |
Numerical Methods, 6 ECTS credits.
/Numeriska metoder/
For:
KeBi
TB
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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:
Within the area of scientific computing algorithms for solution of mathematical problems in technology and science are developed. The student should acquire knowledge of basic concepts within the field and also get acquainted with some algorithms, including the solution of models in biology and chemistry, such as population dynamics, predator-prey models, and chemical reactions. After completing this course the student should be able to
- choose and apply numerical methods for solving given numerical problems
- be able to use some built in Matlab routines for solving problems
- write Matlab programs for calculation and visualization
- analyse the influence of errors in a computed result
- use simple experiments with Matlab in order to analyse the qualities of a numerical method and also determine a method's arithmetic complexity and order of accuracy
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Calculus, Linear Algebra and Introduction to 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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Organisation:
The theory is presented in the lectures.
The ability to explain and separate terms and concepts in computational mathematics, the ability to use numerical algorithms and the ability to estimate he accuracy of calculated results are trained during exercise time.
The computer exercises investigate numerical properties of algorithms and software. Computer exercises includes a few smaller projects.
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Course contents:
- Error Analysis: error propagation, cancellation, floating point arithmetic
- Non-linear Equations: bisection method, Newton-Raphson's method, secant method, error estimation, fixed point iteration, rate of convergence
- Curve fitting: least squares method, Newton's interpolating polynomial, spline interpolation
- Numerical differentiation and integration: difference approximation, Richardson extrapolation,
trapezoidal rule, Simpson's formula, order of accuracy
- Linear algebra: Gaussian elimination, pivoting, LU-decomposition, condition number and perturbation theory, arithmetical complexity, overdetermined linear systems
- Differential equations, systems of initial value problems: Runge-Kutta methods, the trapezoidal method, stability, ode23
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Course literature:
L Eldén, L Wittmeyer-Koch: Numeriska beräkningar- analys och illustrationer med Matlab. Studentlitteratur.
From the department: exercises, formulary, computer assignments
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Examination: |
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Computer examination
Computer exercises
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4 ECTS
2 ECTS
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Computer exercises includes miniprojects, written reports and seminars. |
Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Ingegerd Skoglund
Examiner: Ingegerd Skoglund
Course Syllabus in Swedish
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