Differential Equations

The course is included in the programs Physics and Mathematics - bachelor, and Applied Physics and Mathematics - master (5-years). It may also be taken independent of study program.

This course covers the elementary theory of ordinary and partial differential equations. It is useful to all science students. Covers equations of the first order, systems of linear equations, series solutions, numerical methods for ordinary differential equations, separation of variables for partial differential equations and Fourier series.

Applicants from Nordic countries:

Generell studiekompetanse og følgende spesielle opptakskrav: Matematikk R1 og i tillegg enten:

• Matematikk R2

• Fysikk 1 + 2 eller

• Kjemi 1+ 2 eller

• Biologi 1 + 2 eller

• Informasjonsteknologi 1 +2 eller

• Geofag 1 + 2 eller

• Teknologi og forskningslære 1 + 2

International applicants: Higher Education Entrance Qualification and certified language requirements in English. A list of the requirements for the Higher Education Entrance Qualification in Norway can be found on the Norwegian Agency for Quality Assurance in Education website - nokut.no

Recommended prerequisites is MAT-1030 Vectorcalculus and MAT-1020 Linear Algebra or equal.

Application code is 9197.

After the course the student should be able to

• Solve first order linear and certain types of non-linear differential equations.
• Classify stability of equilibrium for first order differential equations with parameters.
• Know existence/uniqueness theorem for initial value problem of differential equations.
• Know the concept of linearly independent solutions and particular solutions of n-th order linear differential equations and be able to superpose solutions.
• Solve linear differential equations with power series around ordinary points.
• Classify linar and almost linear autonomous systems of differential equations with stability of equilibrium.
• Solve systems of linear differential equations with constant coeffisients.
• Make face portraits and direction fields for autonomous systems in dimenstion 2.
• Know basic theory for Fourier series and use this to solve differential equations..
• Use the method of separtation of variables on simple partial diferential equations with boundary and initial value conditions that lead to development of Fourier series.
• Use Sturm-Liouville eigenvalue theory on standard problems from separation of variables.

Anbefalte forkunnskaper

MAT-1020 Linear algebra, MAT-1030 Vector Calculus

If you pass the examination in this course, you will get an reduction in credits (as stated below), if you previously have passed the following courses:

• MA-221 Ordinary differential equations 6 ects

Language of instruction and examination

Schedule

This course is open to incoming exchange students.

Study Level: Bachelor's

Admission prerequisites: To take this course, you must first meet the requirements listed in the "Admission requirements" section above.

For details on how to apply for exchange, course selection guidelines, or to contact the Incoming Admissions Team, please visit: Admission for Student Exchange.

Re-sit examination