Numerical Methods in Software and Analysis, Second Edition

**Numerical Methods, Software, and Analysis, Second Edition** introduces science and engineering students to the methods, tools, and ideas of numerical computation. Introductory courses in numerical methods face a fundamental problem-there is too little time to learn too much. This text solves that problem by using high-quality mathematical software. In fact, the objective of the text is to present scientific problem solving using standard mathematical software. This book discusses numerous programs and software packages focusing on the IMSL library (including the PROTRAN system) and ACM Algorithms.The book is organized into three parts. Part I presents the background material. Part II presents the principal methods and ideas of numerical computation. Part III contains material about software engineering and performance evaluation. A uniform approach is used in each area of numerical computation. First, an intuitive development is made of the problems and the basic methods for their solution. Then, relevant mathematical software is reviewed and its use outlined. Many areas provide extensive examples and case studies. Finally, a deeper analysis of the methods is presented as in traditional numerical analysis texts. Key Features\* Emphasizes the use of high-quality mathematical software for numerical computation\* Extensive use of IMSL routines\* Features extensive examples and case studies Numerical Methods, Software, and Analysis, Second Edition introduces science and engineering students to the methods, tools, and ideas of numerical computation. Introductory courses in numerical methods face a fundamental problem-there is too little time to learn too much. This text solves that problem by using high-quality mathematical software. In fact, the objective of the text is to present scientific problem solving using standard mathematical software. This book discusses numerous programs and software packages focusing on the IMSL library (including the PROTRAN system) and ACM Algorithms. The book is organized into three parts. Part I presents the background material. Part II presents the principal methods and ideas of numerical computation. Part III contains material about software engineering and performance evaluation. A uniform approach is used in each area of numerical computation. First, an intuitive development is made of the problems and the basic methods for their solution. Then, relevant mathematical software is reviewed and its use outlined. Many areas provide extensive examples and case studies. Finally, a deeper analysis of the methods is presented as in traditional numerical analysis texts. Key Features * Emphasizes the use of high-quality mathematical software for numerical computation * Extensive use of IMSL routines * Features extensive examples and case studies Content: Front Matter, Page iii Copyright, Page iv PREFACE, Pages xi-xiv 1 - MATHEMATICS AND COMPUTER SCIENCE BACKGROUND, Pages 1-17 2 - NUMERICAL SOFTWARE, Pages 19-37 3 - ERRORS, ROUND-OFF, AND STABILITY, Pages 39-68 4 - MODELS AND FORMULAS FOR NUMERICAL COMPUTATION, Pages 69-92 5 - INTERPOLATION, Pages 93-171 6 - MATRICES AND LINEAR EQUATIONS, Pages 173-261 7 - DIFFERENTIATION AND INTEGRATION, Pages 263-322 8 - NONLINEAR EQUATIONS, Pages 323-409 9 - ORDINARY DIFFERENTIAL EQUATIONS, Pages 411-483 10 - PARTIAL DIFFERENTIAL EQUATIONS, Pages 485-550 11 - APPROXIMATION OF FUNCTIONS AND DATA, Pages 551-632 12 - SOFTWARE PRACTICE, COSTS, AND ENGINEERING, Pages 633-657 13 - SOFTWARE PERFORMANCE EVALUATION, Pages 659-675 14 - THE VALIDATION OF NUMERICAL COMPUTATIONS, Pages 677-684 15 - PROTRAN, Pages 685-703 INDEX, Pages 705-720 Emphasizes the use of high-quality mathematical software for numerical computation. The book discusses numerous programs and software packages focusing on the IMSL library (including the PROTRAN system) and ACM algorithms. Examples and case studies are included.