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 completed studies, the student shall
- be able to account for some important concepts and theorems on ordinary differential equation and on the simplest elliptic, parabolic and hyperbolic partial differential equations, and
- know some relevant applications of ordinary and partial differential equations.

Competence and Skills
After completed studies, the student shall be able to
- account for some fundamental concepts and definitions on ordinary differential equations,
- use exact solution methods for solving linear ordinary differential equations,
- account for the existence and uniqueness theorem on ordinary differential equations,
- account for the most important properties of the wave equation (in one spacial dimension), heat equation (in one spacial dimension), and Laplace equation (in two dimensions), and
- account for some relevant applications of ordinary and partial differential equations that are
the part of the course.

Method of reduction of order. Exact solutions of linear ODE. Harmonic oscillator. Kepler's laws. Picard's theorem. Sturm's theorem. Series solutions. Fourier series. Laplace transforms. Nonlinear systems of ODE. Critical points. Stability. Conservative systems. Periodic solutions. Boundary value problems. Laplace equation. Heat equation. Wave equation. Applications in biology and economy.

Teaching consists of lectures and exercises in computer laboratory.
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).

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

Linear Analysis, 7,5 Credits, Complex Analysis, 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).

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


Reading List and Other Teaching Materials

Required Reading

See this Course Syllabus as PDF