Mathematical Methods and Modelling
Students are expected to have a knowledge of the material covered in a typical first course on ordinary and partial differential equations and complex variable methods. This material is covered in many texts, for instance:

W E Boyce and R C Di Prima, Elementary Differential Equations and Boundary Value Problems, Wiley, 7th edition, 2000
orD W Jordan and P Smith, Nonlinear Ordinary Differential Equations, Oxford, 3rd edition, 1999, Chs 1&2

H A Priestley, Introduction to Complex Analysis, Clarendon Press, 1990
orA Jeffrey, Complex Analysis and Applications, CRC, 1992

E Kreyszig, Advanced engineering mathematics, Wiley, 1993, Chs. 6.16.8.18.11,9.19.9,10.110.5,10.11,12.112.8, 13.113.6,14.114.8,15.115.4.
orC M Bender and J A Orszag, Advanced mathematical methods for scientists and engineers McGraw Hill, 1978, Chs. 1,3,6. (Ordinary differential equations and asymptotic expansions)
orF B Hildebrand, Methods of Applied Mathematics, Dover, 1992, Chs 2&3

W Strauss, Partial Differential Equations: An Introduction, Wiley, 1992
orW E Williams, Partial Differential Equations, OUP, 1980
Introductions to mathematical modelling are given in:

S Howison, Practical Applied Mathematics, CUP, 2005

A B Tayler, Mathematical Models in Applied Mechanics, OUP, 1985

A C Fowler, Mathematical Models in The Applied Sciences CUP, 1997
Numerical Analysis
A good knowledge of Calculus of one and several variables and of Linear Algebra is assumed and some acquaintance with elementary Numerical Analysis as found in the books below, for example, is desirable.

E Süli & D Mayers, An Introduction to Numerical Analysis, CUP, 2003,

K E Atkinson, An Introduction to Numerical Analysis, Wiley, 2nd edition, 1989,

S D Conte and C de Boor, Elementary Numerical Analysis McGrawHill, 3rd edition, 1980,

W Gautschi, Numerical Analysis: An Introduction, Birkhauser, 1977,

A Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, 1996

G M Phillips and P J Taylor, Theory and Applications of Numerical Analysis, Academic Press, 2nd edition, 1996,

A Quarteroni, R Sacco and F Saleri, Numerical Mathematics, Springer, 2000,

J Stoer and R Bulirsch, Introduction to Numerical Analysis, SpringerVerlag, 1993