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Ordinary Differential Equations and Dynamical Systems, 6 credits
Ordinära differentialekvationer och dynamiska system, 6 hp
TATA71
Main field of study
Mathematics Applied MathematicsCourse level
First cycleCourse type
Programme courseExaminer
Stefan RauchDirector of studies or equivalent
Jesper ThorénEducation components
Preliminary scheduled hours: 64 hRecommended self-study hours: 96 h
Available for exchange students
YesECV = Elective / Compulsory / Voluntary
Main field of study
Mathematics, Applied MathematicsCourse level
First cycleAdvancement level
G2XCourse offered for
- Energy-Environment-Management
- Mechanical Engineering, M Sc in Engineering
- Applied Physics and Electrical Engineering - International, M Sc in Engineering
- Applied Physics and Electrical Engineering, M Sc in Engineering
- Mathematics, Bachelor´s Programme
Entry requirements
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.
Prerequisites
Linear Algebra, Calculus one variable, Calculus several variables (or their equivalent).Intended learning outcomes
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.
Course content
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.
Teaching and working methods
Lectures, problem classes and computer exercises.
Examination
| UPG1 | Assignments | 2 credits | U, G |
| TEN1 | Written examination | 4 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Matematiska institutionenDirector of Studies or equivalent
Jesper ThorénExaminer
Stefan RauchCourse website and other links
http://www.mai.liu.se/und/kurser/index-amne-tm.htmlEducation components
Preliminary scheduled hours: 64 hRecommended self-study hours: 96 h
Course literature
Additional literature
Books
- Edwards & Penney, Differential equations. Computing and Modelling (3 ed.eller senare.)
Other
- Kurt Hansson, Föreläsningar om ordinära differentialekvationer (pdf-dokument)
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| UPG1 | Assignments | 2 credits | U, G |
| TEN1 | Written examination | 4 credits | U, 3, 4, 5 |
Regulations (apply to LiU in its entirety)
The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.
LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.
Additional literature
Books
Edwards & Penney, Differential equations. Computing and Modelling (3 ed.eller senare.)
Other
Kurt Hansson, Föreläsningar om ordinära differentialekvationer (pdf-dokument)
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
X
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X
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X
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TEN1
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| 1.2 Fundamental engineering knowledge (G1X level) |
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
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X
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X
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TEN1
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| 2.2 Experimentation, investigation, and knowledge discovery |
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
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X
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X
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TEN1
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| 2.5 Ethics, equity, and other responsibilities |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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| 3.2 Communications |
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X
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| 3.3 Communication in foreign languages |
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS | ||||||
| 5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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