spring 2016
MAT-2200 Differential Equations - 10 ECTS
Course content
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.Objectives of the course
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.
Assessment
Written final exam of 4 hours duration, counting 100 %.
Assessment scale: Letter grades A-F.
Re-sit examination:
Students having failed the last ordinary examination are offered a re-sit examination early in the following semester, if the course is compulsory in their study programme.
Postponed examination:
Students with valid grounds for absence will be offered a postponed examination early in the following semester.
- Utfyllende bestemmelser for eksamener ved Fakultet for naturvitenskap og teknologi (only in Norwegian)
- Regulations for examinations at the University of Tromsø
Coursework requirements
A passing grade is required on the mandatory homework sets for permission to take the exam.
Recommended reading/syllabus
Syllabus for MAT-2200 Differential Equations, spring 2016
UiT The Arctic University of Norway, Department of Mathematics and Statistics
Textbook: Edwards and Penney: Differential Equations and Boundary Value Problems. Computing and Modeling. Fourth edition, Pearson 2008.
Syllabus:
Chapter 1: The whole.
Chapter 2: 2.2, 2.4, 2.5.
Chapter 3: 3.1, 3.2, 3.3, 3.5, 3.6.
Chapter 4: 4.1, 4.3.
Chapter 5: All except 5.3.
Chapter 6: 6.1, 6.2.
Chapter 7: Omitted.
Chapter 8: 8.1, 8.2.
Chapter 9: The whole.
Chapter 10: 10.1
Recomended textbook for matlab:
D. Hanselmann and B. Littlefield: Mastering MATLAB7.
Pearson 2005.
Materials allowed during final examination:
Rottmann's tables
Approved statistical tables
Two A4-sheets (both sides) of own notes
Approved calculator.
Error rendering component
- About the course
- Campus: Tromsø |
- ECTS: 10
- Course code: MAT-2200
- Responsible unit
- Institutt for matematikk og statistikk
- Kontaktpersoner
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