Numerical Analysis, 10/e (AE-Paperback)

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

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商品描述

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)

《數值分析》是一本深受推崇的教材,介紹了現代數值逼近技術的理論和應用,適用於修讀一學期或兩學期數值分析課程的學生。本書只需要具備微積分的先修知識,作者解釋了逼近技術何時、為什麼以及如何運作,以及在某些情況下為何會失敗。大量的例子和練習有助於培養學生的直覺,並展示了數值分析在數學、計算、工程和物理科學等重要日常問題中的實際應用。這本書是30多年前為了服務多樣化的本科生讀者而創作的第一本數值分析教材,至今仍然是這一重要且實用主題的權威介紹。

新版《數值分析》的特點包括:
- 本書的設計使得教師可以靈活選擇他們希望涵蓋的主題,選擇所需的理論嚴謹程度,並決定哪些應用對他們的課程最合適或最有趣。
- 本書中的算法設計適用於各種軟件包和編程語言,讓用戶能夠充分利用計算能力進行逼近。本書的附帶網站提供了Maple、Mathematica和MATLAB的工作表,以及C、FORTRAN、Java和Pascal的程式。
- 練習題集包括來自工程學以及物理、計算、生物和社會科學等多個領域的應用問題。
- 本書幾乎每個概念都有例子加以說明。此外,透過2500多個經過班級測試的練習,加強了概念和例子,範圍從方法和算法的基本應用到理論的推廣和擴展。

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)

目錄

1. 數學基礎和誤差分析。

2. 一元方程的解法。

3. 插值和多項式逼近。

4. 數值微分和積分。

5. 常微分方程的初值問題。

6. 解線性系統的直接方法。

7. 矩陣代數中的迭代技術。

8. 逼近理論。

9. 近似特徵值。

10. 非線性方程組的數值解法。

11. 常微分方程的邊值問題。

12. 偏微分方程的數值解法。