A Simple Introduction to Numerical Analysis

Volume 2: Interpolation and Approximation

Author: R.D Harding,D.A Quinney

Publisher: CRC Press

ISBN: 9780852741542

Category: Mathematics

Page: 172

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Approximation techniques are widely used in mathematics and applied physics, as exact solutions are frequently impossible to obtain. A Simple Introduction to Numerical Analysis, Volume 2: Interpolation and Approximation extends the first volume to consider problems in interpolation and approximation. Topics covered include the construction of interpolating functions, the determination of polynomial and rational function approximations, numerical quadrature, and the solution of boundary value problems in ordinary differential equations. As with the previous volume, the text is integrated with a software package that allows the reader to work through numerous examples. It is also possible to use the software to consider problems that are beyond the scope of the text. The authors' expertise in combining text and software has resulted in a very readable work.
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A Short Introduction to Numerical Analysis

Author: M. V. Wilkes

Publisher: CUP Archive

ISBN: 9780521094122

Category: Mathematics

Page: 84

View: 5651

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This short book sets out the principles of the methods commonly employed in obtaining numerical solutions to mathematical equations and shows how they are applied in solving particular types of equations. Now that computing facilities are available to most universities, scientific and engineering laboratories and design shops, an introduction to numerical method is an essential part of the training of scientists and engineers. A course on the lines of Professor Wilkes's book is given to graduate or undergraduate students of mathematics, the physical sciences and engineering at many universities and the number will increase. By concentrating on the essentials of his subject and giving it a modern slant, Professor Wilkes has written a book that is both concise and that covers the needs of a great many users of digital computers; it will serve also as a sound introduction for those who need to consult more detailed works.
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An Introduction to Numerical Analysis

Author: Endre Süli,David F. Mayers

Publisher: Cambridge University Press

ISBN: 9780521007948

Category: Mathematics

Page: 433

View: 4968

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Introduction to numerical analysis combining rigour with practical applications. Numerous exercises plus solutions.
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A Theoretical Introduction to Numerical Analysis

Author: Victor S. Ryaben'kii,Semyon V. Tsynkov

Publisher: CRC Press

ISBN: 9781584886075

Category: Mathematics

Page: 552

View: 2223

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A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on how to efficiently represent mathematical models for computer-based study. An accessible yet rigorous mathematical introduction, this book provides a pedagogical account of the fundamentals of numerical analysis. The authors thoroughly explain basic concepts, such as discretization, error, efficiency, complexity, numerical stability, consistency, and convergence. The text also addresses more complex topics like intrinsic error limits and the effect of smoothness on the accuracy of approximation in the context of Chebyshev interpolation, Gaussian quadratures, and spectral methods for differential equations. Another advanced subject discussed, the method of difference potentials, employs discrete analogues of Calderon’s potentials and boundary projection operators. The authors often delineate various techniques through exercises that require further theoretical study or computer implementation. By lucidly presenting the central mathematical concepts of numerical methods, A Theoretical Introduction to Numerical Analysis provides a foundational link to more specialized computational work in fluid dynamics, acoustics, and electromagnetism.
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A Brief Introduction to Numerical Analysis

Author: Eugene E. Tyrtyshnikov

Publisher: Springer Science & Business Media

ISBN: 0817681361

Category: Mathematics

Page: 202

View: 5562

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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.
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Introduction to Numerical Analysis

Second Edition

Author: F. B. Hildebrand

Publisher: Courier Corporation

ISBN: 0486318559

Category: Mathematics

Page: 669

View: 6513

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Well-known, respected introduction, updated to integrate concepts and procedures associated with computers. Computation, approximation, interpolation, numerical differentiation and integration, smoothing of data, more. Includes 150 additional problems in this edition.
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An Introduction to Numerical Methods

A MATLAB Approach, Third Edition

Author: Abdelwahab Kharab,Ronald B. Guenther

Publisher: CRC Press

ISBN: 1439869006

Category: Mathematics

Page: 576

View: 1884

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Highly recommended by CHOICE, previous editions of this popular textbook offered an accessible and practical introduction to numerical analysis. An Introduction to Numerical Methods: A MATLAB® Approach, Third Edition continues to present a wide range of useful and important algorithms for scientific and engineering applications. The authors use MATLAB to illustrate each numerical method, providing full details of the computer results so that the main steps are easily visualized and interpreted. New to the Third Edition A chapter on the numerical solution of integral equations A section on nonlinear partial differential equations (PDEs) in the last chapter Inclusion of MATLAB GUIs throughout the text The book begins with simple theoretical and computational topics, including computer floating point arithmetic, errors, interval arithmetic, and the root of equations. After presenting direct and iterative methods for solving systems of linear equations, the authors discuss interpolation, spline functions, concepts of least-squares data fitting, and numerical optimization. They then focus on numerical differentiation and efficient integration techniques as well as a variety of numerical techniques for solving linear integral equations, ordinary differential equations, and boundary-value problems. The book concludes with numerical techniques for computing the eigenvalues and eigenvectors of a matrix and for solving PDEs. CD-ROM Resource The accompanying CD-ROM contains simple MATLAB functions that help students understand how the methods work. These functions provide a clear, step-by-step explanation of the mechanism behind the algorithm of each numerical method and guide students through the calculations necessary to understand the algorithm. Written in an easy-to-follow, simple style, this text improves students’ ability to master the theoretical and practical elements of the methods. Through this book, they will be able to solve many numerical problems using MATLAB.
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Introduction to numerical analysis

Author: Alastair Wood

Publisher: Addison Wesley

ISBN: N.A

Category: Mathematics

Page: 349

View: 504

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Author Alastair Wood provides a clear and concise book for novice numerical analysts. Computer based experiments allow readers to learn by doing. Methods are developed with sufficient background, allowing readers to see why a method works and when a method does not work. Wood offers an introduction to the more basic theoretical elements, as well as generating practical skills. Computer skills and real applications are stressed as Wood explores such topics as the Taylor Series, Maclaurin Series, Jacobi Iteration and Gauss-Seidel iteration. For novice Numerical Analysts.
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Introduction to Numerical Analysis

Author: J. Stoer,R. Bulirsch

Publisher: Springer Science & Business Media

ISBN: 038721738X

Category: Mathematics

Page: 746

View: 9138

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New edition of a well-known classic in the field; Previous edition sold over 6000 copies worldwide; Fully-worked examples; Many carefully selected problems
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