Computational Mathematics II, 7.5 credits

Learning outcomes

Knowledge and understanding
After the course the student should

• know and be able to use the most important methods for ill-posed linear problems, interpolation and approximation in R^n,
• know and be able to use the most imporant stochastic methods for simulation and calculation, and
• know some common application areas for computational mathematics.

Skills
After the course the student should

• be able to identify, analyse and numerically solve ill posed linear systems of equations and linear least squares problems,
• be able to use and analyse methods for interpolation and approximation with piecwise polynomials and Bezier curves,
• be able to use and analyse stochastic methods,
• be able to use and analyse the FFT, and
• be able to use and analyse the QR method.

Content

Regularization of ill-posed linear equation systems and linear leasts squares probems. Truncated SVD. L-curve. Cross validation. Applications on integral equations. Interpolation and approximation with piecewise polynomials in several variables. Error analysis. Algorithms for constructing Bezier-curves. Applications to CAD. Monte-Carlo methods with applications. Numerical methods for differential equations using randomwalk. FFT with error analysis and complexity. FFT with error and complexity analysis and applications to signal analysis. QR method. Sustainable calculations.

Examinations and grades

Examination, 7.5 credits (Code: A001)
Grades used are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

According to the Higher Education Ordinance, Chapter 6, Section 18, a grade is to be awarded on the completion of a course, unless otherwise prescribed by the university. The university may determine which grading system is to be used. The grade must be determined by a teacher specifically nominated by the university (the examiner).

In accordance with university regulations on grading systems for first and second-cycle courses and study programmes (Vice-Chancellor’s decision ORU 2018/00929), one of the following grades is to be used: fail (U), pass (G) or pass with distinction (VG). For courses included in an international master’s programme (60 or 120 credits) or offered to the university’s incoming exchange students, the A to F grading scale is to be used. The vice-chancellor, or a person appointed by them, may decide on exceptions from this provision for a specific course, if there are special grounds for doing so.

The grades used on this course are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

Modes of assessment

• Examination (code A001): Written assignment and oral examination

For students with a documented disability, the university may approve applications for adapted or other modes of assessment.

For further information, see the university's local examination regulations.

Specific entry requirements

Optimization, 7.5 Credits, Differential Equations, 7.5 Credits and Numerical Methods for Differential Equations, 6 Credits.

For further information, see the university's admission regulations.

Other provisions

All or part of the course can be given in English.

Students who have been admitted to and registered on a course have the right to receive tuition and/or supervision for the duration of the time period specified for the particular course to which they were accepted (see, the university's admission regulations (in Swedish)). After that, the right to receive tuition and/or supervision expires.

Reading list and other learning resources

Required reading

Sauer, Timothy (2013)
Numerical Analysis
Pearson

Reference literature

Heath, Michael T. (2002)
Scientific Computing: An Introductory Survey
McGraw-Hill

Material handed out by the Mathematics unit.