Unlike a traditional textbook, this book deals completely with Case Studies and Projects. The Case Studies and Projects involve Mathematical and Computational Methods from the three key areas of ODEs, PDEs and Optimization. The leading author, Dr Caldwell, has had extensive experience of Mathematical Modelling throughout his career in both university teaching and industry and was instructor for a team of three Hong Kong mathematics undergraduate students, one of which was Mr Ng, the second author, who won the first place award, Meritorious, in the 2000 Netease Cup China Undergraduate Mathematical Contest in Modelling (CUMCM). Mathematical Modelling is most effectively taught using a Case Study approach. An important aspect of the book is the use of scientific computer software packages such as MAPLE for symbolic algebraic manipulations, MATLAB for numerical simulation and LINDO for linear programming.