MTH744U / MTH744P - Dynamical Systems - 2023/24
Topic | Name | Description |
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EXTRA TUESDAY REVISION SESSION: WKS 10-12 (PDF) | ||
Dec 19th Revision class PDF | ||
LIVE LECTURE NOTES: WKS 1-4 | Lecture notes for weeks 1 to 4 are here. |
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LIVE LECTURE NOTES: WKS 5 | Lecture notes for weeks 5, 6 and 8 are here. Week 7 was reading week. |
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LIVE LECTURE NOTES: WKS 9 - 12 | Lecture notes for weeks 9,10,11 and 12 will be available here over the next three weeks! Currently Weeks 9,10 and 11 available. |
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MID-TERM TEST & SOLNS | MIDTERM TEST AND SOLUTIONS AVAILABLE HERE |
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LECTURE NOTES (Chapters 1-5 inc.) Ver2.4 (Dec 12th) 2023) | The complete list of chapters for the module are: Chapter 1. Dynamical systems on the line R Chapter 2. Bifurcations of dynamical systems on R Chapter 3. Dynamical systems on the circle S1 Chapter 4. Linear dynamical systems on the plane R2 Chapter 5. Nonlinear dynamical systems on R2 |
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QUIZ -DS fixed points on R, S, RxR | Trial quiz on fixed points on \(\mathbb R, S, R^2\). Answers provided here on Monday 30th October. |
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Week 7 pre-test discussion Tuesday Nov 7th 09.00-10.45 | ||
ANSWERS to QUIZ -DS fixed points on R, S, RxR | Trial quiz on fixed points on \(\mathbb R, S, R^2\). Answers provided here on Monday 30th October. |
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SEMINAR TUTORIAL NOTES WKS 1-12 | Seminar Tutorial Notes are here for weeks the whole term. Week 8 (checking the Mid TEST) is listed separately. |
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Assessment Criteria for the Module | ||
Availability for support of students taking MTH744 | ||
MTH744 Examination 2020/21 and Solutions | ||
MTH744 Examination 2022/23 and Solutions | ||
MTH744 Examination 2021/22 and Solutions | ||
Week 4 - Normal forms of bifurcations | EXERCISES 2 SOLNS (3.1.2, 3.1.4, 3.2.2, 3.2.4, 3.4.4, 3.4.8) | |
EXERCISES 2 VIDEO | ||
Week 5- Dynamical systems on the circle | Tutorial week 5 midterm test revision 28th October, 2022 | |
EXERCISES 3 SOLNS | ||
EXERCISES 3 SOLNS VIDEO | ||
Week 8 - Linear systems -classification | Exercises 4 (GN) | STROGATZ p142 5.1.2, 5.1.3, 5.1.5, 5.1.7, 5.1.9, 5.1.10 ((a),(c),(e)) |
QUIZ24(5) PP1-PP8 phase portraits | You need access to this file for the phase portraits required for QUIZ 5. |
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Week 10 - Nonlinear systems III & IV | Exercise 5 Solutions | Strogatz p.182 (Exercises for Chapter 6 of Strogatz) Ex 6.3.1 Ex 6.3.15 Ex 6.3.16 (a). You can try part (b) by using StreamPlot or equivalent. Ex 6.4.1 Ex 6.5.2 Write the second order equation as a first order system in 2-variables x and y. The "homoclinic orbit" is the trajectory that leaves a saddle point as an unstable manifold (with increasing time) and returns to the fixed point as a stable manifold (see notes for an example). Ex. Investigate the following two systems described in polar coordinates, and sketch their phase portraits: (a) (b) . |
Week 11 - Nonlinear Systems V & VI | Exercises 6 Solutions | |
Nonlinear(Ch5) videos | VIDEO 5.1 Nonlinear Systems | Introduction to nonlinear systems. |
VIDEO 5.2 - Fixed points of nonlinear systems | This video discusses fixed points of nonlinear systems and their linearisations. |
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VIDEO 5.3 - Use of nullclines in planar phase portraits | Use of nullclines in sketching phase portraits. |
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VIDEO 5.4 - Conservative and gradient systems(A) | Conservative and Gradient Systems |
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Live Lecture Note PDFs (complement to the Latex lecture notes) |