Numerical Analysis, 7/e
暫譯: 數值分析,第七版
Richard L. Burden, J. Douglas Faires
- 出版商: brooks/cole
- 出版日期: 2000-12-29
- 售價: $1,078
- 語言: 英文
- 頁數: 841
- 裝訂: Hardcover
- ISBN: 0534382169
- ISBN-13: 9780534382162
-
相關分類:
數值分析 Numerical-analysis
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商品描述
The new Seventh Edition of Burden and Faires' well-respected Numerical Analysis provides a foundation in modern numerical-approximation techniques. Explaining how, why, and when the techniques can be expected to work, the Seventh Edition places an even greater emphasis on building readers' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. Applied problems from diverse areas, such as engineering and physical, computer, and biological sciences, are provided so readers can understand how numerical methods are used in real-life situations. The Seventh Edition has been updated and now addresses the evolving use of technology, incorporating it whenever appropriate.
Table of Contents
1. MATHEMATICAL PRELIMINARIES
Review of Calculus / Round-off Errors and
Computer Arithmetic / Algorithms and C onvergence / Numerical Software
2.
SOLUTIONS OF EQUATIONS IN ONE VARIABLE
The Bisection Method / Fixed-Point
Iteration / The Newton's Method / Error Analy sis for Iterative Methods /
Accelerating Convergence / Zeros of Polynomials and Muller's Method / Survey of
Methods and Software
3. INTERPOLATION AND POLYNOMIAL
APPROXIMATION
Interpolation and the LaGrange Polynomial / Divided Differences
/ Hermite Interp olation / Cubic Spline Interpolation / Parametric Curves /
Survey of Methods and Software
4. NUMERICAL DIFFERENTIATION AND
INTEGRATION
Numerical Differentiation / Richardson's Extrapolation / Elements
of Numerical I ntegration / Composite Numerical Integration / Romberg
Integration / Adaptive Qu adrature Methods / Gaussian Quadrature / Multiple
Integrals / Improper Integrals / Survey of Methods and Software
5.
INITIAL-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
The Elementary
Theory of Initial-Value Problems / Euler's Method / Higher-Order Taylor Methods
/ Runge-Kutta Methods / Error Control and the Runge-Kutta-Fehlber g Method /
Multi-Step Methods / Variable Step-Size Multi-Step Methods / Extrapol ation
Methods / Higher-Order Equations and Systems of Differential Equations / S
tability / Stiff Differential Equations / Survey of Methods and Software
6.
DIRECT METHODS FOR SOLVING LINEAR SYSTEMS
Linear Systems of Equations /
Pivoting Strategies / Linear Algebra and Matrix In version / The Determinant of
a Matrix / Matrix Factorization / Special Types of Matrices / Survey of Methods
and Software
7. ITERATIVE TECHNIQUES IN MATRIX ALGEBRA
Norms of Vectors
and Matrices / Eigenvalues and Eigenvectors / Iterative Techniq ues for Solving
Linear Systems / Error Bounds and Iterative Refinement / The Con jugate Gradient
Method / Survey of Methods and Software
8. APPROXIMATION THEORY
Discrete
Least Squares Approximation / Orthogonal Polynomials and Least Squares
Approximation / Chebyshev Polynomials and Economization of Power Series / Ration
al Function Approximation / Trigonometric Polynomial Approximation / Fast Fourie
r Transforms / Survey of Methods and Software
9. APPROXIMATING
EIGENVALUES
Linear Algebra and Eigenvalues / The Power Method / Householder's
Method / The Q R Algorithm / Survey of Methods and Software
10. NUMERICAL
SOLUTIONS OF NONLINEAR SYSTEMS OF EQUATIONS
Fixed Points for Functions of
Several Variables / Newton's Method / Quasi-Newton Methods / Steepest Descent
Techniques / Homotopy and Continuation Methods / Sur vey of Methods and
Software
11. BOUNDARY-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL
EQUATIONS
The Linear Shooting Method / The Shooting Method for Nonlinear
Problems / Finite -Difference Methods for Linear Problems / Finite-Difference
Methods for Nonlinea r Problems / The Rayleigh-Ritz Method / Survey of Methods
and Software
12. NUMERICAL SOLUTIONS TO PARTIAL DIFFERENTIAL
EQUATIONS
Elliptic Partial-Differential Equations / Parabolic
Partial-Differential Equatio ns / Hyperbolic Partial-Differential Equations / An
Introduction to the Finite-E lement Method / Survey of Methods and Software /
BIBLIOGRAPHY / ANSWERS TO SELEC TED EXERCISES / INDEX
商品描述(中文翻譯)
《Burden 和 Faires 的數值分析》第七版是一本備受尊重的教材,提供了現代數值近似技術的基礎。這一版解釋了這些技術如何、為何以及何時可以預期有效,並更加強調培養讀者的直覺,幫助他們理解所呈現技術的一般有效性及在某些情況下失效的原因。書中提供了來自工程、物理、計算機及生物科學等多個領域的應用問題,讓讀者了解數值方法在現實情況中的應用。第七版已更新,並針對技術的演變使用進行了討論,適當時融入相關內容。
**目錄**
1. 數學初步
微積分回顧 / 四捨五入誤差與計算機算術 / 算法與收斂 / 數值軟體
2. 一元方程的解
二分法 / 固定點迭代 / 牛頓法 / 迭代方法的誤差分析 / 加速收斂 / 多項式的零點與穆勒法 / 方法與軟體概述
3. 插值與多項式近似
插值與拉格朗日多項式 / 分割差商 / 赫爾米特插值 / 三次樣條插值 / 參數曲線 / 方法與軟體概述
4. 數值微分與積分
數值微分 / 理查森外推法 / 數值積分的基本元素 / 複合數值積分 / 羅姆伯格積分 / 自適應求積法 / 高斯求積法 / 多重積分 / 不當積分 / 方法與軟體概述
5. 常微分方程的初值問題
初值問題的基本理論 / 歐拉法 / 高階泰勒方法 / 龍格-庫塔方法 / 誤差控制與龍格-庫塔-費爾伯格方法 / 多步驟方法 / 變步長多步驟方法 / 外推法 / 高階方程與微分方程系統 / 穩定性 / 剛性微分方程 / 方法與軟體概述
6. 解線性系統的直接方法
線性方程組 / 樞軸策略 / 線性代數與矩陣反演 / 矩陣的行列式 / 矩陣分解 / 特殊類型的矩陣 / 方法與軟體概述
7. 矩陣代數中的迭代技術
向量與矩陣的範數 / 特徵值與特徵向量 / 解線性系統的迭代技術 / 誤差界限與迭代精煉 / 共軛梯度法 / 方法與軟體概述
8. 近似理論
離散最小二乘近似 / 正交多項式與最小二乘近似 / 切比雪夫多項式與冪級數的經濟化 / 有理函數近似 / 三角多項式近似 / 快速傅立葉變換 / 方法與軟體概述
9. 近似特徵值
線性代數與特徵值 / 幾何法 / 豪斯霍爾德法 / QR 算法 / 方法與軟體概述
10. 非線性方程系統的數值解
多變數函數的固定點 / 牛頓法 / 擬牛頓方法 / 最速下降技術 / 同倫與延續方法 / 方法與軟體概述
11. 常微分方程的邊值問題
線性射擊法 / 非線性問題的射擊法 / 線性問題的有限差分法 / 非線性問題的有限差分法 / 雷利-里茲法 / 方法與軟體概述
12. 偏微分方程的數值解
橢圓型偏微分方程 / 拋物型偏微分方程 / 超曲型偏微分方程 / 有限元素法簡介 / 方法與軟體概述 / 參考文獻 / 選擇題答案 / 索引