Instructor: John Gemmer
Office: Manchester #388
E-mail: gemmerj@wfu.edu Office Hours: Tuesday 2-3, Wednesday 2-4, Thursday 3-5.
Lecture: MWF: 11:00-11:50, Carswell Hall 101
Textbooks: Meiss, J. D. (2007). Differential dynamical systems. Society for Industrial and Applied Mathematics.
Course Handouts:
1. Syllabus: (.pdf)
2. Homework Policy: (.pdf)
3. Latex Templates
4. Overleaf
5. Rubric for Final Report: (.pdf)
Videos:
1. The Great Lego Race (link)
Mathematica Notebooks:
1. Phase portraits (.nb)
2. Lorenz Equations (.nb)
Matlab Scripts:
Term Paper Projects:
1. Floquet Theory: Sections 2.8, 4.11.
2. Chaotic Dynamics: Section 7.1-7.3.
3. Stable Manifold Theorem and Center Manifold Reductions: Sections 5.4-5.6.
4. Unfolding Vector Fields, Saddle Node Bifurcations and Normal Forms: Sections 8.3-8.5.
5. Homoclinic Bifurcations and the Shilnikov Bifurcation: Sections 8.11-8.15.
6. The Smale Horseshoe and Symbolic Dynamics (external reading).
7. Geometric Singular Perturbation Theory (external reading).
Lecture Notes:
1. Lecture #1: (One Dimensional Dynamics) (.pdf)
2. Lecture #2: (Two Dimensional Dynamics) (.pdf)
3. Lecture #3: (Matrix ODEs) (.pdf)
4. Lecture #4: (Exponentials of Operators) (.pdf)
5. Lecture #5: (Complex and Repeated Eigenvalues) (.pdf)
6. Lecture #6: (Linear Stability) (.pdf)
7. Lecture #7: (Nonautonmous Linear Systems) (.pdf)
8. Lecture #8: (Solving Equations) (.pdf)
9. Lecture #9: (Function Spaces) (.pdf)
10. Lecture #10: (Existence and Uniqueness) (.pdf)
11. Lecture #11: (Gronwall's Inequality) (.pdf)
12. Lecture #12: (Flows) (.pdf)
13. Lecture #13: (Linearization and Stability) (.pdf)
14. Lecture #14: (Topological Conjugacy and Equivalence) (.pdf)
15. Lecture #15: (Attractors and Basins) (.pdf)
16: Lecture #16: (Periodic Orbits and Poincare Maps) (.pdf)
17. Lecture #17: (Conservative Dynamics) (.pdf)
18. Lecture #18: (Hamiltonian Dynamics) (.pdf)
19. Lecture #19: (Poisson Dynamics) (.pdf)
20. Lecture #20: (Action Principle) (.pdf)
Exam Solutions:
1. Exam #1: (solutions.pdf)
2. Exam #2: (solutions.pdf)
Homework Assignments:
1. Homework #1: (Due 01/14/22): (.pdf), (.tex). (solutions.pdf)
2. Homework #2: (Due 01/21/22): (.pdf), (.tex). (solutions.pdf)
3. Homework #3: (Due 01/28/22): (.pdf), (.tex). (solutions.pdf)
4. Homework #4: (Due 02/07/22): (.pdf), (.tex). (solutions.pdf)
5. Homework #5: (Due 02/28/22): (.pdf), (.tex). (solutions.pdf)
6. Homework #6: (Due 03/18/22): (.pdf), (.tex). (solutions.pdf)
7. Homework #7: (Due 03/25/22): (.pdf), (.tex). (solutions.pdf)
8. Homework #8: (Due 04/08/22): (.pdf), (.tex). (solutions.pdf)
9. Homework #9: (Due 04/18/22): (.pdf), (.tex). (solutions.pdf)
10. Homework #10: (Due 04/29/22): (.pdf), (.tex).(solutions.pdf)