COURSE SYLLABUS Chaos and Nonlinear Physics 7.5 credits Kaos och Ickelinjär Fysik Second cycle, F7030T Version Autumn 2010 Sp 1 - Autumn 2011 Sp 1Autumn 2011 Sp 2 - Spring 2013 Sp 4Autumn 2013 Sp 1 - Spring 2014 Sp 4Autumn 2014 Sp 1 - Spring 2021 Sp 4Autumn 2021 Sp 1 - Present Course syllabus valid: Autumn 2021 Sp 1 - PresentThe version indicates the term and period for which this course syllabus is valid. The most recent version of the course syllabus is shown first. Education level Second cycle Grade scale G U 3 4 5 Subject Physics Subject group (SCB) Physics Entry requirementsPhysics 30hp and Linear Algebra. More information about English language requirements SelectionThe selection is based on 20-285 creditsCourse Aim It is well known that all physical systems (except in quantum mechanics) are nonlinear. Former limitations to linear systems was of practical nature, as they generally were the only ones which could be exactly solved. By working with user-friendly computer software like Maple the knowledge gained can be applied to problems that would be impossible to study by "paper and pen alone". To teach basic methods of nonlinear physics, which the student can use in his/her continued education, reserch of future work. Contents 1. The world - a nonlinear system! 2. Introduction to Maple 3. Modelling Nature 4. Nonlinear systems I: Examples from a) Mechanics, b) Population dynamics, c) Electrical circuits, d) Chemical osillations, e) Heartbeats 5. Nonlinear systems II: a) Structure formation, b) Solitons, c) Chaos 6. Topological analysis: a) Singular points, b) Phase-plane analysis, c) Bifurcations 7. Limit-cycles: a) Stability, b) Mathematical theorems 8. Forced oscillations: a) Examples, b) Chaotic oscillations, c)"Strange attractors" d) Chaos in Hamiltonian system 9. Nonlinear mapping: a) Logistic mapping, b) Fix-points and stability, c) Period doubling towards chaos, d) The Lyapunov exponent, e) 2-and 3-dimensional mappings, f) Chaos control 10. Nonlinear partial differential equations: a) Examples, b) Nonlinear superposition, c)Solitary waves d) Numerical simultation, e) Inverse scattering method, f) Solitons Realization Each course occasion´s language and form is stated and appear on the course page on Luleå University of Technology's website. Lectures.Examination If there is a decision on special educational support, in accordance with the Guideline Student's rights and obligations at Luleå University of Technology, an adapted or alternative form of examination can be provided. Hand-in assignments. ExaminerJohan HanssonTransition termsThe course F7030T is equal to F7001TLiterature. Valid from Autumn 2010 Sp 1 (May change until 10 weeks before course start)Nonlinear Physics With Maple for Scientists and Engineers, latest edition R.H. Enns, G.C. McGuire. (Contains CD-ROM). Search books in the library » Course offered byDepartment of Engineering Sciences and MathematicsModules CodeDescriptionGrade scaleHPStatusFrom periodTitle 0002AssignmentsG U 3 4 57.50MandatoryA13 Study guidanceStudy guidance for the course is to be found in our learning platform Canvas before the course starts. Students applying for single subject courses get more information in the Welcome letter. You will find the learning platform via My LTU.Syllabus establishedby Department of Applied Physics and Mechanical Engineering 23 Feb 2010Last revisedby Head Faculty Programme Director Niklas Lehto 17 Feb 2021