Instructor: John Gemmer
Office: Manchester #388
E-mail: gemmerj@wfu.edu Office Hours: T 1-3, W 1-2, Th 1-3
Lecture: MWF: 11:00-11:50, Manchester-Kirby, Room 020
Textbooks: Applied Partial Differential Equations (Logan).
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)
Quiz Solutions:
1. Quiz #1 (.pdf)
2. Quiz #2 (.pdf)
3. Quiz #3 (.pdf)
4. Quiz #4 (.pdf)
5. Quiz #5 (.pdf)
6. Quiz #6 (.pdf)
Exam Solutions:
1. Exam #1 (.pdf)
Matlab Scripts:
Mathematica Notebooks:
1. Heat Equation on the Line (.nb)
2. Method of Characteristics (.nb)
3. Wave Equation on the Line (.nb)
4. Fourier Series Example (.nb)
5. Heat Equation on Bounded Interval (.nb)
6. Steady State Solutions to Heat Equation (.nb)
Lecture Notes:
1. Lecture #1: (Partial Recap of ODEs) (.pdf)
2. Lecture #2 (PDE Models) (.pdf)
3. Lecture #3 (Conservation Laws) (.pdf)
4. Lecture #4 (Method of Characteristics) (.pdf)
5. Lecture #5 (Complex Numbers) (.pdf)
6. Lecture #6 (Fourier Transforms) (.pdf)
7. Lecture #7 (Solving PDEs using Fourier Transforms) (.pdf)
8. Lecture #8 (Solving the Wave Equation on the Line) (.pdf)
9. Lecture #9 (The Fourier Method) (.pdf)
10. Lecture #10 (Convergence of Functions) (.pdf)
11. Lecture #11 (Orthogonal Systems) (.pdf)
12. Lecture #12 (Self-Adjoint Operators) (.pdf)
13. Lecture #13 (Heat Equation on Bounded Domain I) (.pdf)
14. Lecture #14 (Heat Equation on Bounded Domain II) (.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), Solutions (.pdf).
6. Homework #6 (.pdf), Solutions (.pdf).
7. Homework #7 (.pdf), Solutions (.pdf).
8. Homework #8 (.pdf), Solutions (.pdf).
Computational Assignments:
1. Computational Assignment #1 (.pdf).
2. Computational Assignment #2 (.pdf).
Project Topics:
1. Conservation laws and the formation of and shock waves (Logan: Section 1.2, Olver Section 2.3)
2. Heat equation in higher dimensions (Logan: Section 1.7 and 4.6)
3. Sturm-Liouville theory for PDEs with non-constant coefficients (Logan: Section 4.2)
4. Age-structured models of population growth (Logan: Section 5.1)
5. Traveling wave fronts in reaction diffusion equations (Logan: Section 5.2)
6. Equilibria and stability of steady state solutions to reaction diffusion equations (Logan: Section 5.3)
7. Black-Scholes Equation and mathematical finance (Olver: Section 8.1)
8. Dispersion relationships and the formation of solitons (Olver: Section 8.5)
9. The wave equation in two dimensions and nodal curves (Olver: Section 11.6)
10. Electromagnetism and Maxwell's equations (Strauss: Section 13.1)
11. Fluids, accoustics, and water waves (Strauss: Section 13.2 and 14.5)