Perturbation methods, simple boundary layers.

Sturm-Liouville systems; integral equations, eigenfunctions.

Partial differential equations: waves and shocks, similarity solutions.

- A.C. Fowler 2005 Techniques of applied mathematics.
Mathematical Institute lecture notes.
Additional reading:

- S.D. Howison 2005 Practical applied mathematics: modelling, analysis, approximation. C.U.P.
- J.P. Keener 2000 Principles of applied mathematics: transformation and
approximation, revised edition. Perseus Books, Cambridge, Mass.
Useful modelling books are:

- R. Haberman 1998 Mathematical models. SIAM, Philadelphia.
- A.C. Fowler 1997 Mathematical Models in the Applied Sciences. CUP, Cambridge.
- A.B. Tayler 1986 Mathematical Models in Applied Mechanics. OUP, Oxford.
Mathematical techniques are in:

- E.J. Hinch 1991 Perturbation Methods. CUP, Cambridge.
- D.W. Jordan and P. Smith 1999 Nonlinear Ordinary Differential Equations, 3rd ed. OUP, Oxford.
- E.A. Coddington and N. Levinson 1972 Theory of ordinary differential equations. Tata McGraw-Hill, New Delhi.
- I. Stakgold 2000 Boundary value problems of mathematical physics, vol. I. SIAM, Philadelphia.

- Combustion and hysteresis (notes).
- Stability and oscillations.
*(pp. 43-46, 49-54)* - Poincaré-Lindstedt method. Van der Pol
equation.
*(pp. 34-40)* - Derivation of Sturm-Liouville systems.
*(pp. 64-70)* - Sturm-Liouville theory.
*(pp. 70-75)Sturm-Liouville theory continued.**(pp. 70-75)Comparison methods.**(pp. 75-76)* *Integral equations.**(pp. 79-83)Eigenfunction expansions.**(pp. 83-86)**Variational methods.**(pp. 86-89)**Waves and shocks.**(pp. 92-102)**Burgers' equation, transition layer.**(pp. 105-109)**Similarity solutions. The heat equation.**(pp. 112-115)**Porous medium equation.**(pp. 116-119)*