In this book, we are going to examine various types of numerical problems and develop techniques for solving them. We will gradually build up the necessary tools and use a number of case studies to:
(i) illustrate the process of formulating a problem, by which we mean translating from an intuitive idea of the problem by writing it down mathematically,
(ii) motivate and develop algorithms to solve problems, that is, descriptions of operations that can be implemented in software to take a problem specification and return a solution, and
(iii) illustrate how to match the formulation of the problem to the capabilities of available algorithms, involving, in some cases, transformation of the problem from its initial formulation. ...