Numerical Analysis

This book is primarily intended for undergraduates in mathematics, the physical sciences and engineering. It introduces students to most of the techniques forming the core component of courses in numerical analysis. The text is divided into eight chapters which are largely self-contained. However, with a subject as intricately woven as mathematics, there is inevitably some interdependence between them. The level of difficulty varies and, although emphasis is firmly placed on the methods themselves rather than their analysis, we have not hesitated to include theoretical material when we consider it to be sufficiently interesting. However, it should be possible to omit those parts that do seem daunting while still being able to follow the worked examples and to tackle the exercises accompanying each section. Familiarity with the basic results of analysis and linear algebra is assumed since these are normally taught in first courses on mathematical methods. For reference purposes a list of theorems used in the text is given in the appendix. Front Matter....Pages i-vii Introduction....Pages 1-7 Linear algebraic equations....Pages 8-42 Non-linear algebraic equations....Pages 43-70 Eigenvalues and eigenvectors....Pages 71-128 Methods of approximation theory....Pages 129-189 Numerical differentiation and integration....Pages 190-232 Ordinary differential equations: initial value problems....Pages 233-264 Ordinary differential equations: boundary value problems....Pages 265-276 Back Matter....Pages 277-326