Instructor: John Gemmer
Office: Manchester #388
E-mail: gemmerj@wfu.edu Office Hours: Tuesday 9-10, Wednesday 11:30-12:30, Thursday 1-3
Lecture: MWF: 10:00-10:50, Manchester 018
Textbooks: See syllabus.
Course Handouts:
1. Syllabus: (.pdf)
2. Homework Policy: (.pdf)
3. Example Homework Solutions: (.pdf)
4. Latex Templates
5. Overleaf
6. Written Report Rubric (.pdf)
7. Presentation Rubric (.pdf)
Mathematica Notebooks:
Matlab Scripts:
1. Euler's Method Main Script (.m)
2. Lotka Volterra Function (.m)
Quiz Solutions:
1. Quiz #1 (.pdf).
2. Quiz #2 (.pdf).
3. Quiz #3 (.pdf).
Exam Solutions:
1. Exam #1 (.pdf)
Lecture Notes:
1. Lecture #1: (Intro Example) (.pdf)
2. Lecture #2: (Flows on the Line) (.pdf)
3. Lecture #3: (Existence and Uniqueness) (.pdf)
4. Lecture #4: (Potentials and Impossibility of Oscillations) (.pdf)
5. Lecture #5: (SIS Model and Transcritical Bifurcations) (.pdf)
6. Lecture #6: (Saddle Node and Pitchfork Bifurcations) (.pdf)
7. Lecture #7: (Model of Fishing in a Lake) (.pdf)
8. Lecture #8: (Bead on a Rotating Hoop) (.pdf)
9. Lecture #9: (Flows on a Circle and Fireflies) (.pdf)
10. Lecture #10: (Introduction to Phase Plane) (.pdf)
11. Lecture #11: (Linear Systems) (.pdf)
12. Lecture #12: (Love and War) (.pdf)
13. Lecture #13: (Phase Portraits and Linearization) (.pdf)
14. Lecture #14: (Lotka Volterra Systems) (.pdf)
15. Lecture #15: (Polar Coordinates) (.pdf)
16. Lecture #16: (Conserved Quantities) (.pdf)
17. Lecture #17: (Index Theory) (.pdf)
18. Lecture #18: (Eliminating Limit Cycles) (.pdf)
19. Lecture #19: (Limit Cyles) (.pdf)
20. Lecture #20: (Co-dimension 1 bifurcations) (.pdf)
21. Lecture #21: (Global bifurcations) (.pdf)
22. Lecture #22: (Motion on a Torus) (.pdf)
23. Bonus Lecture: (Numerical Solutions to ODEs) (.pdf)
Homework Assignments:
1. Homework #1 (.pdf), Solutions (.pdf).
2. Homework #2 (.pdf), Solutions (.pdf).
3. Homework #3 (.pdf), Solutions (.pdf).
4. Homework #4 (.pdf), Solutions (.pdf).
5. Homework #5 (.pdf).
Potential Projects from Research Papers:
1. A mathematical model for the profit-driven abandonment of restaurant tipping.
2. Chaos and scheduling Buses.
3. Cats, rats, and seabirds.
4. Water mites and mosquitoes.
5. Epidemic dynamics on adaptive networks.
6. Modeling the decline of religous affliation.
7. Modeling language death.
8. Mathematical model of gender bias in professional hierarchies
9. Rock, paper, scissors and the evolution of lizards.
10. Modeling romantic love
11. Low dimensional model of hurricane formation.
12. The power of true believers.
13. Sychrony in frogs.
14. Predator prey food chains with adaptation.
15. Particle interactions and pattern formation.
16. Oscillators that sync and swarm.
17.
Rolling swarms of locusts.
18. Rise and fall of political parties.
19. Synchronization of cows.
20. Modeling insect outbreaks.
21. Sychrony in fireflys.
22. Oscillations in chemical reactions
23. Modeling the loss of arctic sea ice.
24. Modeling the foraging of ants.
25. Modeling the ocean's circulation.
26. Modeling El-Nino.
27. Modeling the ocean's carbon cycle.
28. Forcasting Elections.
Potential Projects from Textbooks:
Topics in Mathematical Modeling, K.K. Tung:
1. Chapter 9: Snowball Earth and Global Warming.It's a Nonlinear World, Richard Enns:
2. Chapter 10: Marriage and Divorce.
3. Chapter 12: El Nino and the Southern Oscillation.
4. Chapter 14: Collapsing Bridges: Broughton and Tacoma Narrows.
1. Chapter 5: Motion.
2. Chapter 6: Sports.
3. Chapter 7: Electromagnetism.
4. Chapter 8: Weather.
5. Chapter 9: Chemistry.
6. Chapter 10: Disease.
7. Chapter 11: War.