Computational Mathematics

Computational mathematics is the study of methods for the approximate, numerical solution of mathematically posed problems. The objective of this book is to introduce the fundamental concepts on which computational mathematics is based. A key skill is to be able to abstract a problem and formulate it in such a way that the computational power of the computer may be brought to bear on the problem in an effective and efficient way. There is a need for the "computational point of view" which will focus on the concepts of approximation and algorithms, and which is not merely a translation of a mathematical algorithm onto the computer. This book is designed to develop the "computational point of view", while still dealing with elementary topics accessible to first year university students or advanced high school students with a knowledge of elementary calculus. The emphasis is on the construction of computational algorithms rather than on mathematical analysis of the methods used.