| TATA71 |
Ordinary Differential Equations and Dynamical Systems, 6 ECTS credits.
/Ordinära differentialekvationer och dynamiska system/
For:
EM
M
Mat
Y
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Prel. scheduled
hours: 64
Rec. self-study hours: 96
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G2
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Aim:
To teach students the more advanced theory of ordinary differential equations and of dynamical systems and to give an introduction to modern computer based facilities (Maple). After a completed course, the student will be able to:
- Use some of the classical methods for solving special ordinary differential equations.
- Analyze the stability of equilibrium points for non linear autonomic systems via both linearisation and Liapunov functions.
- Formulate and analyze differential equations using simple models from physics, chemistry and biology.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Linear Algebra, Calculus one variable, Calculus several variables (or their equivalent).
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Organisation:
Lectures, problem classes and computer exercises.
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Course contents:
Exact equations, integrating factor. Solving differential equations in Maple. Picards existence theorem. Linear differential equations with variable coefficients. Systems of linear differential equations, fundamental systems of solutions. Resolvent matrix and exponential matrix. Linearization. Stability theory for planar autonomous systems. Liapunov's theorem.
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Course literature:
Edwards & Penney, Differential equations. Computing and Modelling (3 ed. or later)
Kurt Hansson, Lectures om ordinary differential equations (pdf-document, in swedish)
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Examination: |
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Written examination
Assignements
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4 ECTS
2 ECTS
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Course language is Swedish/English.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Stefan Rauch
Link to the course homepage at the department
Course Syllabus in Swedish
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