Numerical Analysis, 10/e (AE-Paperback)
暫譯: 數值分析，第10版 (AE-平裝本)

Richard L. Burden , Douglas Faires , Annette M. Burden

Numerical Analysis, 10/e (AE-Paperback)

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Description
This well-respected text introduces the theory and application of modern numerical approximation techniques to students taking a one- or two-semester course in numerical analysis. Providing an accessible treatment that only requires a calculus prerequisite, the authors explain how, why, and when approximation techniques can be expected to work-and why, in some situations, they fail. A wealth of examples and exercises develop students' intuition, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. The first book of its kind when crafted more than 30 years ago to serve a diverse undergraduate audience, Burden, Faires, and Burden's NUMERICAL ANALYSIS remains the definitive introduction to a vital and practical subject.

What's New
*The design of the text gives instructors flexibility in choosing topics they wish to cover, selecting the level of theoretical rigor desired, and deciding which applications are most appropriate or interesting for their classes.
*The algorithms in the text are designed to work with a wide variety of software packages and programming languages, allowing maximum flexibility for users to harness computing power to perform approximations. The book's companion website offers Maple, Mathematica, and MATLAB worksheets, as well as C, FORTRAN, Java, and Pascal programs.
*The exercise sets include many applied problems from diverse areas of engineering, as well as from the physical, computer, biological, and social sciences.
Virtually every concept in the text is illustrated by examples. In addition, concepts and examples are reinforced by more than 2500 class-tested exercises ranging from elementary applications of methods and algorithms to generalizations and extensions of the theory.

商品描述(中文翻譯)

描述

這本備受尊敬的教材介紹了現代數值近似技術的理論和應用，適合修習一或兩學期數值分析課程的學生。該書提供了一個易於理解的處理方式，只需具備微積分的先修知識，作者解釋了何時、如何以及為何可以期待近似技術的有效性，以及在某些情況下它們為何失敗。大量的範例和練習題幫助學生培養直覺，並展示了該主題在數學、計算、工程和物理科學等日常問題中的實際應用。這本書是30多年前為多元化的本科生觀眾而編寫的第一本此類書籍，Burden、Faires和Burden的數值分析仍然是這一重要且實用主題的權威入門書。

新內容

* 本書的設計使得教師在選擇希望涵蓋的主題、選擇所需的理論嚴謹程度以及決定哪些應用最適合或最有趣的課程時具有靈活性。

* 書中的算法設計能與各種軟體包和程式語言兼容，讓使用者能夠靈活運用計算能力來進行近似計算。本書的伴隨網站提供了Maple、Mathematica和MATLAB的工作表，以及C、FORTRAN、Java和Pascal的程式。

* 練習題集包含來自不同工程領域的許多應用問題，以及來自物理、計算、生物和社會科學的問題。

幾乎每個概念都通過範例進行說明。此外，概念和範例還通過超過2500個經過課堂測試的練習題得到強化，這些練習題涵蓋了從方法和算法的基本應用到理論的概括和擴展。

目錄大綱

Table of Contents
1. MATHEMATICAL PRELIMINARIES AND ERROR ANALYSIS.
2. SOLUTIONS OF EQUATIONS IN ONE VARIABLE.
3. INTERPOLATION AND POLYNOMIAL APPROXIMATION.
4. NUMERICAL DIFFERENTIATION AND INTEGRATION.
5. INITIAL-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS.
6. DIRECT METHODS FOR SOLVING LINEAR SYSTEMS.
7. ITERATIVE TECHNIQUES IN MATRIX ALGEBRA.
8. APPROXIMATION THEORY.
9. APPROXIMATING EIGENVALUES.
10. NUMERICAL SOLUTIONS OF NONLINEAR SYSTEMS OF EQUATIONS.
11. BOUNDARY-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS.
12. NUMERICAL SOLUTIONS TO PARTIAL DIFFERENTIAL EQUATIONS.

目錄大綱(中文翻譯)

Table of Contents

1. MATHEMATICAL PRELIMINARIES AND ERROR ANALYSIS.

2. SOLUTIONS OF EQUATIONS IN ONE VARIABLE.

3. INTERPOLATION AND POLYNOMIAL APPROXIMATION.

4. NUMERICAL DIFFERENTIATION AND INTEGRATION.

5. INITIAL-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS.

6. DIRECT METHODS FOR SOLVING LINEAR SYSTEMS.

7. ITERATIVE TECHNIQUES IN MATRIX ALGEBRA.

8. APPROXIMATION THEORY.

9. APPROXIMATING EIGENVALUES.

10. NUMERICAL SOLUTIONS OF NONLINEAR SYSTEMS OF EQUATIONS.

11. BOUNDARY-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS.

12. NUMERICAL SOLUTIONS TO PARTIAL DIFFERENTIAL EQUATIONS.

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