This textbook demonstrates the power of mathematics in solving practical, scientific, and technical problems through mathematical modelling techniques. It has been designed specifically for final year undergraduate and graduate students, and springs from the author's extensive teaching experience. The text is combined with twenty-one carefully ordered problems taken from real situations, and students are encouraged to develop the skill of constructing their own models of new situations. Table of Contents 1:Problem formulation 2:Wave motion 3:Elliptic problems 4:Diffusion 5:Asymptotic methods for non-linear problems Bibliography Index