Ordinary Differential Equations and Dynamical Systems, 6 credits (TATA71)

Ordinära differentialekvationer och dynamiska system, 6 hp

Main field of study

Mathematics Applied Mathematics

Level

First cycle

Course type

Programme course

Examiner

Stefan Rauch

Director of studies or equivalent

Jesper Thorén

Available for exchange students

Yes
Course offered for Semester Period Timetable module Language Campus VOF
6CEMM Energy-Environment-Management 7 (Autumn 2017) 2 3 Swedish/English Linköping v
6CMMM Mechanical Engineering, M Sc in Engineering 7 (Autumn 2017) 2 3 Swedish/English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 2 3 Swedish/English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2017) 2 3 Swedish/English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 2 3 Swedish/English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2017) 2 3 Swedish/English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 2 3 Swedish/English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2017) 2 3 Swedish/English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 2 3 Swedish/English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2017) 2 3 Swedish/English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 2 3 Swedish/English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2017) 2 3 Swedish/English Linköping v
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering 7 (Autumn 2017) 2 3 Swedish/English Linköping v
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2017) 2 3 Swedish/English Linköping v
6KMAT Mathematics, Bachelor´s Programme 3 (Autumn 2017) 2 3 Swedish/English Linköping v
6KMAT Mathematics, Bachelor´s Programme (Computer Science) 3 (Autumn 2017) 2 3 Swedish/English Linköping v
6KMAT Mathematics, Bachelor´s Programme (Modelling and Optimization in Economics) 3 (Autumn 2017) 2 3 Swedish/English Linköping v
6KMAT Mathematics, Bachelor´s Programme (Mathematics) 3 (Autumn 2017) 2 3 Swedish/English Linköping v
6KMAT Mathematics, Bachelor´s Programme (Applied Mathematics) 3 (Autumn 2017) 2 3 Swedish/English Linköping v

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G2X

Course 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

TEN1Written examinationU, 3, 4, 54 credits
UPG1AssignmentsU, G2 credits

Grades

Four-grade scale, LiU, U, 3, 4, 5

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén

Examiner

Stefan Rauch

Education components

Preliminary scheduled hours: 64 h
Recommended 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)

Additional literature

Books

Edwards & Penney, Differential equations. Computing and Modelling (3 ed.eller senare.)

Other

Kurt Hansson, Föreläsningar om ordinära differentialekvationer (pdf-dokument)
TEN1 Written examination U, 3, 4, 5 4 credits
UPG1 Assignments U, G 2 credits

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. 

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