Afternotes On Numerical Analysis

This book presents the central ideas of modern numerical analysis in a vivid and straightforward fashion with a minimum of fuss and formality. Stewart designed this volume while teaching an upper-division course in introductory numerical analysis. To clarify what he was teaching, he wrote down each lecture immediately after it was given. The result reflects the wit, insight, and verbal craftmanship which are hallmarks of the author. Simple examples are used to introduce each topic, then the author quickly moves on to the discussion of important methods and techniques. With its rich mixture of graphs and code segments, the book provides insights and advice that help the reader avoid the many pitfalls in numerical computation that can easily trap an unwary beginner. Written by a leading expert in numerical analysis, this book is certain to be the one you need to guide you through your favorite textbook.

This book presents the central ideas of modern numerical analysis in a vivid and straightforward fashion with a minimum of fuss and formality. Stewart designed this volume while teaching an upper-division course in introductory numerical analysis.

Afternotes on Numerical Analysis is the result of the author writing down his notes immediately after giving each lecture.

In this follow-up to Afternotes on Numerical Analysis (SIAM, 1996) the author continues to bring the immediacy of the classroom to the printed page. Like the original undergraduate volume, Afternotes Goes to Graduate School is the result of the author writing down his notes immediately after giving each lecture; in this case the afternotes are the result of a follow-up graduate course taught by Professor Stewart at the University of Maryland. The algorithms presented in this volume require deeper mathematical understanding than those in the undergraduate book, and their implementations are not trivial. Stewart uses a fresh presentation that is clear and intuitive as he covers topics such as discrete and continuous approximation, linear and quadratic splines, eigensystems, and Krylov sequence methods. He concludes with two lectures on classical iterative methods and nonlinear equations.

A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.

The aim of this book is to provide a simple and useful introduction for the fresh students into the vast field of numerical analysis. Like any other introductory course on numerical analysis, this book contains the basic theory, which in the present text refers to the following topics: linear equations, nonlinear equations, eigensystems, interpolation, approximation of functions, numerical differentiation and integration, stochastics, ordinary differential equations and partial differential equations. Because the students need to quickly understand why the numerical methods correctly work, the proofs of theorems were shorted as possible, insisting more on ideas than on a lot of algebra manipulation. The included examples are presented with a minimum of complications, emphasizing the steps of the algorithms. The numerical methods described in this book are illustrated by computer programs written in C. Our goal was to develop very simple programs which are easily to read and understand by students. Also, the programs should run without modification on any compiler that implements the ANSI C standard. Because our intention was to easily produce screen input-output (using, scanf and printf), in case of WINDOWS visual programming environments, like Visual C++ (Microsoft) and Borland C++ Builder, the project should be console-application. This will be not a problem for DOS and LINUX compilers. If this material is used as a teaching aid in a class, I would appreciate if under such circumstances, the instructor of such a class would send me a note at the address below informing me if the material is useful. Also, I would appreciate any suggestions or constructive criticism regarding the content of these lecture notes.

Numerical analysis provides the theoretical foundation for the numerical algorithms we rely on to solve a multitude of computational problems in science. Based on a successful course at Oxford University, this book covers a wide range of such problems ranging from the approximation of functions and integrals to the approximate solution of algebraic, transcendental, differential and integral equations. Throughout the book, particular attention is paid to the essential qualities of a numerical algorithm - stability, accuracy, reliability and efficiency. The authors go further than simply providing recipes for solving computational problems. They carefully analyse the reasons why methods might fail to give accurate answers, or why one method might return an answer in seconds while another would take billions of years. This book is ideal as a text for students in the second year of a university mathematics course. It combines practicality regarding applications with consistently high standards of rigour.

Engineering reliability concerns failure data analysis, the economics of maintenance policies, and system reliability. This textbook develops the use of probability and statistics in engineering reliability and maintenance problems. The author uses probability models in the analysis of failure data, decisions relative to planned maintenance, and prediction relative to preliminary design. Some of the outstanding features include the analysis of failure data for both continuous and discrete probability from a finite population perspective, probability models derived from engineering considerations, an introduction to influence diagrams and decision making, and use of the operational Bayesian approach. The approach is fresh and interesting; it is motivated from problems in engineering and physical sciences and uses examples to illustrate the methodology. These examples, along with the use of real failure time data, will help the reader apply the techniques to real industrial situations.