Matrices and Determinants: Definition of an m x n matrix, matrix addition, subtraction transposition, multiplication by a scalar, matrix multiplication, square matrices, determinants and properties. Solution of Equations, inverse matrices
Partial Differential Equations: Introduction to 1st and 2nd order equations: Classification (Hyperbolic, Parabolic and Elliptic), Solution of Hyperbolic and Parabolic equations e.g. DíAlembertís solution. Method of characteristic lines: Applications .
Laplace Transforms: Introduction, theory, convolution, inverse. Applications to ODEs, Impulse and step function forcing.
Tutorial problems: Revision Notes and Exercises with solutions are available:
E. Kreyszig. Advanced Engineering Mathematics, John Wiley, 7th Edition, 1993.
K.A. Stroud and D.J. Booth. Engineering Mathematics, 5th Edition, Palgrave, Basingstoke, 2001.
Mathematics by Computer:
Introductory Mathematica packages for graphing functions, algebra and calculus using a computer are available via Beginning Mathematica and an introductory book on differential equations using Mathematica is:
M.L. Abell and J.P. Braselton. Differential Equations with Mathematica, 2nd Edition, Academic Press, San Diego 1997.A more advanced comprehensive treatment is:
A. Gray, M. Mezzino and M.A. Pinsky. Introduction to Ordinary Differential Equations with Mathematica, Springer-Telos, Santa Clara 1997.For MATLAB users, an engineering-orientated book is:
A.Biran and M. Breiner. MATLAB for Engineers, Addison-Wesley, Wokingham 1995.