Advanced Engineering Mathematics, 10/e (Update) (Taiwan Custom Version)(Paperbck)
暫譯: 高等工程數學，第10版（更新版）（台灣客製版）（平裝本）

Erwin Kreyszig

Advanced Engineering Mathematics, 10/e (Update) (Taiwan Custom Version)(Paperbck)

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• Parts of Chap. 1 on first-order ODEs are rewritten. More emphasis on modeling, also new block diagram explaining this concept in Sec. 1.1. Early introduction of Euler's method in Sec. 1.2 to familiarize student with basic numerics. More examples of separable ODEs in Sec. 1.3.
• For Chap. 2, on second-order ODEs, note the following changes: For ease of reading, the first part of Sec. 2.4, which deals with setting up the mass-spring system, has been rewritten; also some rewriting in Sec. 2.5 on the Euler-Cauchy equation.
• Substantially shortened Chap. 5, Series Solutions of ODEs. Special Functions: combined Secs. 5.1 and 5.2 into one section called "Power Series Method," shortened material in Sec. 5.4 Bessel's Equation (of the first kind), removed Sec. 5.7 (Sturm-Liouville Problems) and Sec. 5.8 (Orthogonal Eigenfunction Expansions) and moved material into Chap. 11 (see "Major Changes" above).
• New equivalent definition of basis (Sec. 7.4).
• In Sec. 7.9, completely new part on composition of linear transformations with two new examples. Also, more detailed explanation of the role of axioms, in connection with the definition of vector space.
• New table of orientation (opening of Chap. 8 "Linear Algebra: Matrix Eigenvalue Problems") where eigenvalue problems occur in the book. More intuitive explanation of what an eigenvalue is at the begining of Sec. 8.1.
• Better definition of cross product (in vector differential calculus) by properly identifying the degenerate case (in Sec. 9.3).
• Chap. 11 on Fourier Analysis extensively rearranged: Secs. 11.2 and 11.3 combined into one section (Sec. 11.2), old Sec. 11.4 on complex Fourier Series removed and new Secs. 11.5 (Sturm-Liouville Problems) and 11.6 (Orthogonal Series) put in (see "Major Changes" above). New problems (new!) in problem set 11.9 on discrete Fourier transform.
• New section 12.5 on modeling heat flow from a body in space by setting up the heat equation. Modeling PDEs is more difficult so we separated the modeling process from the solving process (in Sec. 12.6).
• Introduction to Numerics rewritten for greater clarity and better presentation; new Example 1 on how to round a number. Sec. 19.3 on interpolation shortened by removing the less important central difference formula and giving a reference instead.
• Large new footnote with historical details in Sec. 22.3, honoring George Dantzig, the inventor of the simplex method.
• Traveling salesman problem now described better as a "difficult" problem, typical of combinatorial optimization (in Sec. 23,2]." More careful explanation on how to compute the capacity of a cut set in Sec. 23.6 (Flows on Networks).
• Additional problems for Chapters '16-19, 22 and 23 are available on line at www.wiley.com/go/global/kreyszig.

商品描述(中文翻譯)

• 第一章關於一階常微分方程（ODE）的部分已重新編寫。更強調建模，並在第1.1節中新增了說明此概念的方塊圖。第1.2節早期引入歐拉法（Euler's method），以幫助學生熟悉基本數值方法。第1.3節增加了更多可分離ODE的範例。

• 第二章關於二階常微分方程的變更如下：為了提高可讀性，第2.4節的第一部分（處理質量-彈簧系統的建立）已重新編寫；第2.5節關於歐拉-柯西方程（Euler-Cauchy equation）也進行了一些重寫。

• 第5章，常微分方程的級數解，已大幅縮短。特殊函數：將第5.1節和第5.2節合併為一節，稱為「冪級數法（Power Series Method）」，縮短第5.4節貝塞爾方程（Bessel's Equation，第一類），刪除第5.7節（斯圖姆-柳維爾問題）和第5.8節（正交特徵函數展開），並將相關內容移至第11章（見上方「主要變更」）。

• 新的等價定義的基底（basis）（第7.4節）。

• 在第7.9節，完全新增了線性變換的組合部分，並提供了兩個新範例。此外，對公理的角色進行了更詳細的解釋，與向量空間的定義相關聯。

• 新的方向表（第8章「線性代數：矩陣特徵值問題」的開頭），說明書中出現特徵值問題的地方。在第8.1節開始時，對特徵值的直觀解釋更加清晰。

• 更好的交叉積（cross product）定義（在向量微分計算中），通過正確識別退化情況（在第9.3節）。

• 第11章傅立葉分析經過廣泛重組：第11.2節和第11.3節合併為一節（第11.2節），舊的第11.4節關於複數傅立葉級數已刪除，並新增第11.5節（斯圖姆-柳維爾問題）和第11.6節（正交級數）（見上方「主要變更」）。在問題集11.9中新增了關於離散傅立葉變換的新問題（新！）。

• 新增第12.5節，通過建立熱方程來建模空間中物體的熱流。建模偏微分方程（PDE）更具挑戰性，因此我們將建模過程與解題過程分開（在第12.6節）。

• 數值方法的介紹已重新編寫，以提高清晰度和更好的呈現；新增範例1，說明如何進行數字四捨五入。第19.3節關於插值的內容已縮短，刪除了不太重要的中心差分公式，並提供了參考。

• 第22.3節新增了大量的註腳，包含歷史細節，以紀念簡單形法的發明者喬治·丹齊格（George Dantzig）。

• 旅行推銷員問題現在更好地描述為「困難」問題，典型的組合優化問題（在第23.2節）。在第23.6節（網絡流）中，對如何計算切割集的容量進行了更仔細的解釋。

• 第16-19章、22章和23章的附加問題可在線上獲得，網址為 www.wiley.com/go/global/kreyszig。

目錄大綱

PART A Ordinary Differential Equations (ODEs)
CHAPTER 1 First-Order ODEs
CHAPTER 2 Second-Order Linear ODEs
CHAPTER 3 Higher Order Linear ODEs
CHAPTER 4 Systems of ODEs. Phase Plane. Qualitative Methods
CHAPTER 5 Series Solutions of ODEs. Special Functions
CHAPTER 6 Laplace Transforms
PART B Linear Algebra. Vector Calculus
CHAPTER 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems
CHAPTER 8 Linear Algebra: Matrix Eigenvalue Problems
CHAPTER 9 Vector Differential Calculus. Grad, Div, Curl
CHAPTER 10 Vector Integral Calculus. Integral Theorems
PART C Fourier Analysis. Partial Differential Equations (PDEs)
CHAPTER 11 Fourier Analysis
CHAPTER 12 Partial Differential Equations (PDEs)
PART D Complex Analysis
CHAPTER 13 Complex Numbers and Functions. Complex Differentiaion
CHAPTER 14 Complex Integration
CHAPTER 15 Power Series, Taylor Series
CHAPTER 16 Laurent Series. Residue Integration
CHAPTER 17 Conformal Mapping
CHAPTER 18 Complex Analysis and Potential Theory
PART E Numeric Analysis
Software
CHAPTER 19 Numerics in General
CHAPTER 20 Numeric Linear Algebra
CHAPTER 21 Numerics for ODEs and PDEs
PART F Optimization, Graphs
CHAPTER 22 Unconstrained Optimization. Linear Programming
CHAPTER 23 Graphs. Combinatorial Optimization

目錄大綱(中文翻譯)

PART A Ordinary Differential Equations (ODEs)

CHAPTER 1 First-Order ODEs

CHAPTER 2 Second-Order Linear ODEs

CHAPTER 3 Higher Order Linear ODEs

CHAPTER 4 Systems of ODEs. Phase Plane. Qualitative Methods

CHAPTER 5 Series Solutions of ODEs. Special Functions

CHAPTER 6 Laplace Transforms

PART B Linear Algebra. Vector Calculus

CHAPTER 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems

CHAPTER 8 Linear Algebra: Matrix Eigenvalue Problems

CHAPTER 9 Vector Differential Calculus. Grad, Div, Curl

CHAPTER 10 Vector Integral Calculus. Integral Theorems

PART C Fourier Analysis. Partial Differential Equations (PDEs)

CHAPTER 11 Fourier Analysis

CHAPTER 12 Partial Differential Equations (PDEs)

PART D Complex Analysis

CHAPTER 13 Complex Numbers and Functions. Complex Differentiaion

CHAPTER 14 Complex Integration

CHAPTER 15 Power Series, Taylor Series

CHAPTER 16 Laurent Series. Residue Integration

CHAPTER 17 Conformal Mapping

CHAPTER 18 Complex Analysis and Potential Theory

PART E Numeric Analysis

Software

CHAPTER 19 Numerics in General

CHAPTER 20 Numeric Linear Algebra

CHAPTER 21 Numerics for ODEs and PDEs

PART F Optimization, Graphs

CHAPTER 22 Unconstrained Optimization. Linear Programming

CHAPTER 23 Graphs. Combinatorial Optimization

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