Numerical Analysis

Author : J. Stoer,R. Bulirsch
Publisher : Springer Science & Business Media
Page : 674 pages
File Size : 45,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475722727

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Introduction to Numerical Analysis by J. Stoer,R. Bulirsch Pdf

On the occasion of this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions: Due to their special properties, their flexibility, and the availability of well-tested programs for their computation, B-splines play an important role in many applications. Also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. Even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for handling sparse matrices. We will explain some of these techniques in connection with the Cholesky algorithm for solving positive definite linear systems. The chapter on eigenvalue problems was enlarged by a section on the Lanczos algorithm; the sections on the LR and QR algorithm were rewritten and now contain a description of implicit shift techniques. In order to some extent take into account the progress in the area of ordinary differential equations, a new section on implicit differential equa tions and differential-algebraic systems was added, and the section on stiff differential equations was updated by describing further methods to solve such equations.

Author : Larkin Ridgway Scott
Publisher : Princeton University Press
Page : 342 pages
File Size : 47,7 Mb
Release : 2011-04-18
Category : Mathematics
ISBN : 9781400838967

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Numerical Analysis by Larkin Ridgway Scott Pdf

Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases. The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject. Presents the mathematical foundations of numerical analysis Explains the mathematical details behind simulation software Introduces many advanced concepts in modern analysis Self-contained and mathematically rigorous Contains problems and solutions in each chapter Excellent follow-up course to Principles of Mathematical Analysis by Rudin

Author : Atkinson
Publisher : John Wiley & Sons
Page : 580 pages
File Size : 48,6 Mb
Release : 2009-07
Category : Electronic
ISBN : 8126508027

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Elementary Numerical Analysis (3Rd Ed.) by Atkinson Pdf

Offering a clear, precise, and accessible presentation, complete with MATLAB programs, this new Third Edition of Elementary Numerical Analysis gives students the support they need to master basic numerical analysis and scientific computing. Now updated and revised, this significant revision features reorganized and rewritten content, as well as some new additional examples and problems.The text introduces core areas of numerical analysis and scientific computing along with basic themes of numerical analysis such as the approximation of problems by simpler methods, the construction of algorithms, iteration methods, error analysis, stability, asymptotic error formulas, and the effects of machine arithmetic.· Taylor Polynomials · Error and Computer Arithmetic · Rootfinding · Interpolation and Approximation · Numerical Integration and Differentiation · Solution of Systems of Linear Equations · Numerical Linear Algebra: Advanced Topics · Ordinary Differential Equations · Finite Difference Method for PDEs

Author : Herbert B. Keller
Publisher : Courier Dover Publications
Page : 417 pages
File Size : 48,6 Mb
Release : 2018-11-14
Category : Mathematics
ISBN : 9780486828343

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Numerical Methods for Two-Point Boundary-Value Problems by Herbert B. Keller Pdf

Elementary yet rigorous, this concise treatment is directed toward students with a knowledge of advanced calculus, basic numerical analysis, and some background in ordinary differential equations and linear algebra. 1968 edition.

Author : Anne Greenbaum,Tim P. Chartier
Publisher : Princeton University Press
Page : 471 pages
File Size : 50,8 Mb
Release : 2012-04-01
Category : Mathematics
ISBN : 9781400842674

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Numerical Methods by Anne Greenbaum,Tim P. Chartier Pdf

A rigorous and comprehensive introduction to numerical analysis Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results. The book gives instructors the flexibility to emphasize different aspects—design, analysis, or computer implementation—of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book also includes polynomial interpolation at Chebyshev points, use of the MATLAB package Chebfun, and a section on the fast Fourier transform. Supplementary materials are available online. Clear and concise exposition of standard numerical analysis topics Explores nontraditional topics, such as mathematical modeling and Monte Carlo methods Covers modern applications, including information retrieval and animation, and classical applications from physics and engineering Promotes understanding of computational results through MATLAB exercises Provides flexibility so instructors can emphasize mathematical or applied/computational aspects of numerical methods or a combination Includes recent results on polynomial interpolation at Chebyshev points and use of the MATLAB package Chebfun Short discussions of the history of numerical methods interspersed throughout Supplementary materials available online

Author : Tobin A. Driscoll,Richard J. Braun
Publisher : SIAM
Page : 583 pages
File Size : 42,5 Mb
Release : 2017-12-21
Category : Science
ISBN : 9781611975086

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Fundamentals of Numerical Computation by Tobin A. Driscoll,Richard J. Braun Pdf

Fundamentals of Numerical Computation?is an advanced undergraduate-level introduction to the mathematics and use of algorithms for the fundamental problems of numerical computation: linear algebra, finding roots, approximating data and functions, and solving differential equations. The book is organized with simpler methods in the first half and more advanced methods in the second half, allowing use for either a single course or a sequence of two courses. The authors take readers from basic to advanced methods, illustrating them with over 200 self-contained MATLAB functions and examples designed for those with no prior MATLAB experience. Although the text provides many examples, exercises, and illustrations, the aim of the authors is not to provide a cookbook per se, but rather an exploration of the principles of cooking. The authors have developed an online resource that includes well-tested materials related to every chapter. Among these materials are lecture-related slides and videos, ideas for student projects, laboratory exercises, computational examples and scripts, and all the functions presented in the book. The book is intended for advanced undergraduates in math, applied math, engineering, or science disciplines, as well as for researchers and professionals looking for an introduction to a subject they missed or overlooked in their education.?

Author : Brian Sutton
Publisher : SIAM
Page : 431 pages
File Size : 49,6 Mb
Release : 2019-04-18
Category : Mathematics
ISBN : 9781611975703

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Numerical Analysis by Brian Sutton Pdf

This textbook develops the fundamental skills of numerical analysis: designing numerical methods, implementing them in computer code, and analyzing their accuracy and efficiency. A number of mathematical problems?interpolation, integration, linear systems, zero finding, and differential equations?are considered, and some of the most important methods for their solution are demonstrated and analyzed. Notable features of this book include the development of Chebyshev methods alongside more classical ones; a dual emphasis on theory and experimentation; the use of linear algebra to solve problems from analysis, which enables students to gain a greater appreciation for both subjects; and many examples and exercises. Numerical Analysis: Theory and Experiments is designed to be the primary text for a junior- or senior-level undergraduate course in numerical analysis for mathematics majors. Scientists and engineers interested in numerical methods, particularly those seeking an accessible introduction to Chebyshev methods, will also be interested in this book.

Author : Kendall Atkinson,Weimin Han
Publisher : Springer Science & Business Media
Page : 576 pages
File Size : 50,9 Mb
Release : 2007-06-07
Category : Mathematics
ISBN : 9780387287690

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Theoretical Numerical Analysis by Kendall Atkinson,Weimin Han Pdf

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). Thedevelopmentofnewcoursesisanaturalconsequenceofahighlevelof excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Ma- ematical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.

Author : Walter Gautschi
Publisher : Springer Science & Business Media
Page : 588 pages
File Size : 49,9 Mb
Release : 2011-12-07
Category : Mathematics
ISBN : 9780817682590

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Numerical Analysis by Walter Gautschi Pdf

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.

Author : Kenneth Lange
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 52,9 Mb
Release : 2010-05-17
Category : Business & Economics
ISBN : 9781441959454

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Numerical Analysis for Statisticians by Kenneth Lange Pdf

Numerical analysis is the study of computation and its accuracy, stability and often its implementation on a computer. This book focuses on the principles of numerical analysis and is intended to equip those readers who use statistics to craft their own software and to understand the advantages and disadvantages of different numerical methods.

Author : John Gregory,Don Redmond
Publisher : Jones & Bartlett Publishers
Page : 352 pages
File Size : 43,7 Mb
Release : 1994
Category : Mathematics
ISBN : UOM:39015032965322

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Introduction to Numerical Analysis by John Gregory,Don Redmond Pdf

Author : Eugene E. Tyrtyshnikov
Publisher : Springer Science & Business Media
Page : 205 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681364

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A Brief Introduction to Numerical Analysis by Eugene E. Tyrtyshnikov Pdf

A logically organized advanced textbook, which turns the reader into an active participant by asking questions, hinting, giving direct recommendations, comparing different methods, and discussing "pessimistic" and "optimistic" approaches to numerical analysis. Advanced students and graduate students majoring in computer science, physics and mathematics will find this book helpful.

Author : J. Douglas Faires,Richard L. Burden
Publisher : Brooks Cole
Page : 616 pages
File Size : 55,9 Mb
Release : 1998
Category : Mathematics
ISBN : UOM:39015041023386

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Numerical Methods by J. Douglas Faires,Richard L. Burden Pdf

This text emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. The authors provide a sophisticated introduction to various appropriate approximation techniques; they show students why the methods work, what type of errors to expect, and when an application might lead to difficulties; and they provide information about the availability of high-quality software for numerical approximation routines The techniques covered in this text are essentially the same as those covered in the Sixth Edition of these authors' top-selling Numerical Analysis text, but the emphasis is much different. In Numerical Methods, Second Edition, full mathematical justifications are provided only if they are concise and add to the understanding of the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the student that the method is reasonable both mathematically and computationally.

Author : Anthony Ralston,Philip Rabinowitz
Publisher : Courier Corporation
Page : 644 pages
File Size : 43,6 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 048641454X

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A First Course in Numerical Analysis by Anthony Ralston,Philip Rabinowitz Pdf

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.

Author : Timo Heister,Leo G. Rebholz,Fei Xue
Publisher : Walter de Gruyter GmbH & Co KG
Page : 193 pages
File Size : 49,6 Mb
Release : 2019-03-18
Category : Mathematics
ISBN : 9783110573336

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Numerical Analysis by Timo Heister,Leo G. Rebholz,Fei Xue Pdf

Numerical analysis deals with the development and analysis of algorithms for scientific computing, and is in itself a very important part of mathematics, which has become more and more prevalent across the mathematical spectrum. This book is an introduction to numerical methods for solving linear and nonlinear systems of equations as well as ordinary and partial differential equations, and for approximating curves, functions, and integrals.