Download e-book for iPad: An Introduction to Numerical Methods and Analysis by James F. Epperson

By James F. Epperson

ISBN-10: 1118367596

ISBN-13: 9781118367599

Praise for the First Edition

". . . outstandingly attractive in regards to its variety, contents, concerns of necessities of perform, number of examples, and exercises."—Zentralblatt MATH

". . . rigorously based with many certain labored examples."—The Mathematical Gazette

The Second Edition of the very popular An advent to Numerical equipment and Analysis offers an absolutely revised consultant to numerical approximation. The e-book is still available and expertly publications readers throughout the many on hand suggestions of numerical tools and analysis.

An creation to Numerical tools and research, moment Edition displays the most recent tendencies within the box, contains new fabric and revised workouts, and provides a different emphasis on purposes. the writer sincerely explains how you can either build and assessment approximations for accuracy and function, that are key abilities in various fields. quite a lot of higher-level tools and options, together with new issues similar to the roots of polynomials, spectral collocation, finite point principles, and Clenshaw-Curtis quadrature, are awarded from an introductory standpoint, and the Second Edition additionally features:

  • Chapters and sections that commence with easy, effortless fabric by way of slow assurance of extra complex material
  • Exercises starting from uncomplicated hand computations to demanding derivations and minor proofs to programming exercises
  • Widespread publicity and usage of MATLAB
  • An appendix that includes proofs of varied theorems and different material

The publication is a perfect textbook for college kids in complex undergraduate arithmetic and engineering classes who're drawn to gaining an figuring out of numerical tools and numerical analysis.

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Extra resources for An Introduction to Numerical Methods and Analysis

Sample text

1125351747 x 10~ 6 . Because x is so small, the absolute error in y = 0 as an approximation to x is also small. 2 x 1 0 - 7 , which is decent accuracy in many settings. However, this "approximation" is clearly not a good one. 8886110521 x 107. Because z is so large, the absolute error in almost any approximation will be large, even though almost all of the digits are matched. 8886110517x 107, then we have \z — w\ = 4 x 10~ 3 , hardly very small, even though y matches z to nine decimal digits. The point is that relative error gives a measure of the number of correct digits in the approximation.

Problem 5 asks you to implement this as a subprogram and check it against the intrinsic natural logarithm function on your computer. Can this be improved? Yes, it is possible to construct an equally accurate logarithm approximation that uses fewer computations. Problem 6 asks you to look into this by using a clever combination of logarithm expansions that results in faster convergence. Exercises: 1. Write each of the following in the form x = f x 2" for some / 6 [|, 1]. (a) x = 13; (b) x = 25; (c) x (d) X = 3' io· 2.

A) f{x) = (VxT9-3)x-u, (b) f(x) = x_1(l — cosz); (c) f(x) = (1 — x)~1(\nx — Βΐηπχ); (d) f(x) = ( c o s ^ + x) -cos7r)a; _ 1 ; (e) /(x) = ( e 1 + x - e 1 - I ) ( 2 x ) - 1 . 4. For f(x) = (e x — l)/x, how many terms in a Taylor expansion are needed to get single-precision accuracy (seven-decimal digits) for all x e [0, ^]? How many terms are needed for double-precision accuracy (14 decimal digits) over this same range? 5. Using single-precision arithmetic only, carry out each of the following computations, using first the form on the left side of the equals sign, then using the form on the right side, and compare the two results.

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An Introduction to Numerical Methods and Analysis by James F. Epperson


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