A First Course in Numerical Analysis

Author: Anthony Ralston,Philip Rabinowitz

Publisher: Courier Corporation

ISBN: 9780486414546

Category: Mathematics

Page: 606

View: 1705

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Outstanding text, oriented toward computer solutions, stresses errors in methods and computational efficiency. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter.
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Numerical Analysis

Author: Richard L. Burden,J. Douglas Faires

Publisher: Cengage Learning

ISBN: 0538735643

Category: Numerical analysis

Page: 872

View: 9256

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This well-respected text gives an introduction to the modern approximation techniques and explains how, why, and when the techniques can be expected to work. The authors focus on building students' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. With a wealth of examples and exercises, the text demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. The applications chosen demonstrate concisely how numerical methods can be, and often must be, applied in real-life situations. In this edition, the presentation has been fine-tuned to make the book even more useful to the instructor and more interesting to the reader. Overall, students gain a theoretical understanding of, and a firm basis for future study of, numerical analysis and scientific computing. A more applied text with a different menu of topics is the authors' highly regarded NUMERICAL METHODS, Third Edition.
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Numerical Analysis

A Mathematical Introduction

Author: M. Schatzman,Michelle Schatzman

Publisher: Oxford University Press

ISBN: 9780198508526

Category: Mathematics

Page: 496

View: 9668

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Numerical analysis explains why numerical computations work, or fail. This book is divided into four parts. Part I starts Part I starts with a guided tour of floating number systems and machine arithmetic. The exponential and the logarithm are constructed from scratch to present a new point ofview on questions well-known to the reader, and the needed knowledge of linear algebra is summarized. Part II starts with polynomial approximation (polynomial interpolation, mean-square approximation, splines). It then deals with Fourier series, providing the trigonometric version of least squareapproximations, and one of the most important numerical algorithms, the fast Fourier transform. Any scientific computation program spends most of its time solving linear systems or approximating the solution of linear systems, even when trying to solve non-linear systems. Part III is therefore aboutnumerical linear algebra, while Part IV treats a selection of non-linear or complex problems: resolution of linear equations and systems, ordinary differential equations, single step and multi-step schemes, and an introduction to partial differential equations. The book has been written having inmind the advanced undergraduate students in mathematics who are interested in the spice and spirit of numerical analysis. The book does not assume previous knowledge of numerical methods. It will also be useful to scientists and engineers wishing to learn what mathematics has to say about thereason why their numerical methods work - or fail.
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Numerical Analysis

Author: Tim D. Sauer

Publisher: N.A

ISBN: 9780321461353

Category: Numerical analysis

Page: 669

View: 770

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Numerical Analysis, designed to be used in a one-year course for students in engineering, science and mathematics, helps the student gain a deeper understanding of numerical analysis by highlighting the five major ideas of the discipline: Convergence, Complexity, Conditioning, Compression, and Orthogonality and connecting back to them throughout the text. Each chapter contains a Reality Check, an extended foray into a relevant application area that can be used as a springboard for individual or team projects. MATLAB is used throughout to demonstrate and implement numerical methods.
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Numerical Analysis

Author: Richard Burden,J. Faires

Publisher: Cengage Learning

ISBN: 0534392008

Category: Mathematics

Page: 850

View: 7794

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This well-respected text gives an introduction to the modern approximation techniques and explains how, why, and when the techniques can be expected to work. The authors focus on building students' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. With a wealth of examples and exercises, the text demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. The applications chosen demonstrate concisely how numerical methods can be, and often must be, applied in real-life situations. In this edition, the presentation has been fine-tuned to make the book even more useful to the instructor and more interesting to the reader. Overall, students gain a theoretical understanding of, and a firm basis for future study of, numerical analysis and scientific computing. A more applied text with a different menu of topics is the authors' highly regarded NUMERICAL METHODS, Third Edition. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
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Dynamical Systems and Numerical Analysis

Author: Andrew Stuart,A. R. Humphries

Publisher: Cambridge University Press

ISBN: 9780521645638

Category: Mathematics

Page: 685

View: 7106

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This book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulted as dynamical systems and the convergence and stability properties of the methods are examined. Topics studied include the stability of numerical methods for contractive, dissipative, gradient and Hamiltonian systems together with the convergence properties of equilibria, periodic solutions and strage attractors under numerical approximation. This book will be an invaluable tool for graduate students and researchers in the fields of numerical analysis and dynamical systems.
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Special Volume: Foundations of Computational Mathematics

Author: Phillipe G. Ciarlet

Publisher: Gulf Professional Publishing

ISBN: 9780444512475

Category: Mathematics

Page: 536

View: 6524

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From geometric integration and its applications, and linear programming and condition numbers under the real number computational model, to chaos in finite difference schemes, these essays explore the foundational issues of computational mathematics.
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Numerical Analysis

Author: Walter Gautschi

Publisher: Springer Science & Business Media

ISBN: 0817682597

Category: Mathematics

Page: 588

View: 8516

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Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth. Along with updated references, new biographical notes, and enhanced notational clarity, this second edition includes the expansion of an already large collection of exercises and assignments, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. Perhaps most notably, the edition also comes with a complete solutions manual, carefully developed and polished by the author, which will serve as an exceptionally valuable resource for instructors.
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Numerical Methods

Author: Germund Dahlquist,Åke Björck

Publisher: Courier Corporation

ISBN: 9780486428079

Category: Mathematics

Page: 573

View: 5186

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Practical text strikes balance between students' requirements for theoretical treatment and the needs of practitioners, with best methods for both large- and small-scale computing. Many worked examples and problems. 1974 edition.
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