Applied Mathematics, 7.5 credits

Aims and objectives

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)

Course objectives

Knowledge and Understanding
After completed studies, the student shall have

• knowledge of some of the most central problems and methods of analysis within applied mathematics, and
• knowledge of some important applications within applied mathematics.

Competence and Skills
After completed studies, the student shall be able to,

• do a dimensional analysis and scale problems,
• analyze and solve simpler differential equations and integral equations using series approximation and transforms,
• analyze and solve simpler control problems analytically, and
• analyze and solve simpler dynamical systems analytically.

Main content of the course

Buckinghams Pi-theorem. Scaling of equations. Properties of Fredholms and Volterras integral equations and Sturm-Liouville problems. Greens function. Fouriertransform. Fourierseries. Euler-Lagrange equations. Stability for dynamical systems. Bifurcation theory. Applications.

Teaching methods

Teaching is done in the form of lectures.
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.

Examination methods

Examination, 7.5 credits (Code: A001)
Assignments.

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

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

Grades

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 2019-01-15, ORU 2019/00107), 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).

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

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

Specific entry requirements

Computational Mathematics II, 7.5 Credits, Optimization, 7, 5 Credits.

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

Transfer of credits for previous studies

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).

Other provisions

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

Reading list and other teaching materials

Required Reading

Debnath, Lokenath & Mikusinski, Piotr (2005)
Introduction to Hilbert Spaces with Applications
Academic Pres

distributed material