School of Science and Technology

Course Syllabus

General aims for first cycle education

First-cycle courses and study programmes shall develop:
- the ability of students to make independent and critical assessments
- the ability of students to identify, formulate and solve problems autonomously, and
- the preparedness of students to deal with changes in working life.

In addition to knowledge and skills in their field of study, students shall develop the ability to:
- gather and interpret information at a scholarly level
- stay abreast of the development of knowledge, and
- communicate their knowledge to others, including those who lack specialist knowledge in the field.

(Higher Education Act, Chapter 1, Section 8)

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,
- know and be able to use different computer tools for symbolic calculations,
- know some common application areas for computational mathematics.

Skills
After the course the student should
- be able to identify, analyse and numerically solve linear 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,
- be able to use and analyse Bezier-curves,
- be able to use and analyse stochastic methods for simulation, calculation of integrals and solving differential equations,
- be able to use and analyse the FFT,
- be able to use and analyse multistep methods for ODE.

Regularization of ill posed linear equation systems and linear leasts squares probems. A priori information. Truncated SVD. L-curve. Cross validation. Applicaitons on integral equations. Interpolation and approximation with piecewise polynomials in several variables. Error analysis. Algorithms for construction Bezier-curves. Applications to CAD. Monte-Carlo methods with applications to integrals. Numerical methods for differential equations using randomwalk. FFT with error analysis and complexity. FFT with error and complexity analysis and applications to signal analysis. Multistep methods for initial value ODE. Numerical analysis of methods for initial value ODE.

Teaching in the form of lectures and supervised projects.
The teaching methods may be altered, should only a few students take the course.

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.

For further information, see the university's local examination regulations (in Swedish).

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 prescribe which grading system shall apply. The grade is to be determined by a teacher specifically appointed by the university (an examiner).

According to regulations on grading systems for first- and second-cycle education (vice-chancellor's decision 2010-10-19, reg. no. CF 12-540/2010), one of the following grades is to be used: fail, pass, or pass with distinction. The vice-chancellor or a person appointed by the vice-chancellor may decide on exceptions from this provision for a specific course, if there are special reasons.

Grades used on course are Fail (U), Pass (G) or Pass with Distinction (VG).

The course grading is translated to the ECTS grading scale.

For further information, see the university's local examination regulations (in Swedish).

Optimization, 7,5 Credits, Differential Equations, 7,5 Credits and Numerical Methods for Differential Equations, 7,5 Credits.

For further information, see the university's admission regulations (in Swedish).

Students who have previously completed higher education or other activities are, in accordance with the Higher Education Ordinance, entitled to have these credited towards the current programme, providing that the previous studies or activities meet certain criteria.

For further information, see the university's local credit transfer regulations (in Swedish).

Required Reading

Material som tillhandahålles av enheten för matematik.
Material handed out by the Department of Mathematics.

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