Readings are assigned in the following textbooks:
Required
Logan, J. David. An Introduction to Nonlinear Partial Differential Equations. Hoboken, NJ: Wiley-Interscience, c2008. ISBN: 9780470225950.
Recommended
Logan, J. David. Applied Mathematics. Hoboken, NJ: Wiley-Interscience, c2006. ISBN: 9780471746621.
Howison, Sam. Practical Applied Mathematics: Modelling, Analysis, Approximation. Cambridge, UK; New York, NY: Cambridge University Press, 2005. ISBN: 9780521603690.
Whitham, G. B. Linear and Nonlinear Waves. New York, NY: Wiley, 1974. ISBN: 9780471940906.
Haberman, Richard. Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow: an Introduction to Applied Mathematics. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1998. ISBN: 9780898714081.
Readings about MATLAB
MATLAB on Athena
MATLAB tutorial
Weekly Reading Assignments
The reading assignments for weeks 2 through 14 are from the required book.
Course readings.
| WEEK # |
TOPICS |
READINGS |
| 1 |
Dimensional analysis. Scaling |
Lin, C. C. and L. A. Segel. Mathematics applied to Deterministic Problems in the Natural Sciences. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1988. ISBN: 9780898712292. Chapter 6, Pages 185-224. |
| 2 |
Perturbation methods |
Logan, J. David. Applied Mathematics. Hoboken, NJ: Wiley-Interscience, c2006. ISBN: 9780471746621. Chapter 2, Pages 85-123.
|
| 3 |
Introduction to PDE |
Chapter 1 |
| 4 |
Introduction to PDE (cont.) |
Chapter 1 |
| 5 |
First-order equations and MOC |
Chapter 2 |
| 6 |
First-order equations and MOC (cont.) |
Chapter 2 |
| 7 |
Weak solutions to hyperbolic equations |
Chapter 3 |
| 8 |
Weak solutions to hyperbolic equations (cont.) |
Chapter 3 |
| 9 |
Hyperbolic systems |
Chapter 4 |
| 10 |
Hyperbolic systems (cont.) |
Chapter 4 |
| 11 |
Diffusion and reaction processes |
Chapter 5 |
| 12 |
Diffusion and reaction processes (cont.) |
Chapters 5 and 6 |
| 13 |
Equilibrium models |
Chapter 7 |
| 14 |
Equilibrium models (cont.) |
Chapter 7 |
