Differential Equations, 7.5 credits

Learning outcomes

Knowledge and understanding
After completing the course, the student shall be able to

• explain the basics of the theory of ordinary differential equations and systems of such.

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

• use established methods to solve systems of first order ordinary differential equations as well as linear second order ordinary differential equations,
• apply the theory of linear ordinary differential equations to determine solutions,
• account for and apply Picard's theorem on the existence and uniqueness of solutions,
• use established methods to determine qualitative properties of solutions to systems of ordinary differential equations,
• account for applications of differential equations,
• solve separable partial differential equations using separation of variables, and
• present mathematical theory, methods and solutions to problems.

Evaluation Ability and Approach

After completed studies, the student shall be able to

• assess the reasonableness of results in problem solving.

Content

Picard's theorem of existence and uniqueness, exact solution of first order ordinary differential equations, the theory of linear ordinary differential equations. Laplace transform. Separable partial differential equations. The theory of systems of first order ordinary differential equations. Applications of ordinary and partial differential equations. Mathematical writing.

Examinations and grades

Theory and Problem Solving, 4.5 credits (Code: A002)
Grades used are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

Mathematical Writing, 3 credits (Code: A003)
Grades used are Fail (U) or Pass (G).

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).

Comments on grades

The grade for the examination part Theory and problem solving is given as a grade for the course as a whole, provided that the grade for the examination part Mathematical writing is Passed.

Modes of assessment

• Theory and problem solving (code A002): Written examination
• Mathematical writing (code A003): Written assignment

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

Mathematical Modelling and Problem Solving, 6 Credits and Komplex Analysis, 6 Credits.

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

Other provisions

All or part of the course may 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

Simmons, George F. (latest edition)
Differential Equations with Applications and Historical Notes
CRC Press