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Course Catalog 2010-2011
MAT-35006 Dynamical Systems and Chaos, 6 cr |
Person responsible
Mikko Kaasalainen
Lessons
| Study type | P1 | P2 | P3 | P4 | Summer | Implementations | Lecture times and places |
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Requirements
Exam, problem classes/project work
Principles and baselines related to teaching and learning
Computational implementation alongside the mathematical analysis (computer exercises and program development)
Learning outcomes
Basic knowledge about nonlinear dynamical systems and typical examples of them; the causes and characteristics of chaotic behaviour in Hamiltonian and dissipative systems; fundamental theoretical and computational methods
Content
| Content | Core content | Complementary knowledge | Specialist knowledge |
| 1. | General properties of nonlinear anc chaotic systems, qualitative description and mathematical principles (3) | Mathematical analysis of Hamiltonian and dissipative chaotic systems | Applications in various fields (biology, circuits, mechanics, weather); discrete systems |
Evaluation criteria for the course
Exam 1/2, problem classes/project work 1/2
Assessment scale:
Numerical evaluation scale (1-5) will be used on the course
Study material
| Type | Name | Author | ISBN | URL | Edition, availability, ... | Examination material | Language |
| Book | Differential equations, dynamical systems and an introduction to chaos | Hirsch, Smale, Devaney | 0-12-349703-5 | The first part of the book (chapters 1-7/8) is covered in the course "differential equations" (mat-33500/6), the second part in this course | English | ||
| Book | Perspectives of nonlinear dynamics (Cambridge) | Jackson | English | ||||
| Book | Regular and stochastic dynamics (Springer) | Lichtenberg and Lieberman | English |
Prerequisites
| Course | Mandatory/Advisable | Description |
| MAT-31090 Matriisilaskenta 1 | Mandatory | |
| MAT-33500 Differentiaaliyhtälöt | Mandatory |
Prerequisite relations (Requires logging in to POP)
Correspondence of content
There is no equivalence with any other courses
Additional information
Suitable for postgraduate studies
More precise information per implementation
| Implementation | Description | Methods of instruction | Implementation |
| Introduction to nonlinear dynamical systems and chaotic dynamics |