MATLAB在工程与科学中：数值方法第二版详解

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《数值方法应用于工程与科学：MATLAB第二版》是一本由Ramin S. Esfandiari博士编著的专业书籍，专为工程师和科学家提供使用MATLAB进行数值计算的方法。本书是MATLAB商标所有者The MathWorks, Inc. 授权使用的，但须注意，书中提供的文本和练习可能并不保证其准确性，使用MATLAB软件或相关产品并不构成The MathWorks对特定教学方法或软件使用方式的官方认可。本书第二版详尽探讨了数值计算在工程和科学研究中的应用，通过MATLAB这一强大的工具包，作者展示了如何解决实际问题中的复杂数学模型和方程组。MATLAB作为一种广泛使用的编程语言和环境，其图形用户界面和内置函数库极大地简化了数值分析、线性代数、微分方程求解、优化、统计分析等领域的计算任务。书中内容覆盖了以下关键知识点： 1. **数值分析基础**：介绍了数值逼近、误差分析和收敛性概念，为读者理解数值方法的可靠性和有效性打下基础。 2. **线性代数**：包括矩阵运算、特征值和特征向量、矩阵分解（如LU分解、QR分解等）以及解线性系统等核心内容。 3. **微分方程数值解法**：涵盖了欧拉法、龙格-库塔法、辛普森法则等经典方法，以及用于偏微分方程的有限差分和有限元方法。 4. **优化技术**：讨论了梯度下降法、牛顿法、拟牛顿法和遗传算法等优化算法在MATLAB中的实现。 5. **统计与数据处理**：涉及随机数生成、概率分布、假设检验和回归分析等统计工具在MATLAB中的应用。 6. **实验设计与模拟**：如何使用MATLAB进行模拟实验、参数研究和不确定性量化，以支持科学研究中的决策制定。 7. **实用技巧与示例**：提供了丰富的实战案例，帮助读者掌握MATLAB编程技巧，解决实际问题。《数值方法应用于工程与科学：MATLAB第二版》适合在校学生、研究人员和工程师，不论他们是初学者还是进阶用户，都能从中获益匪浅，提升他们的数值计算能力。该书不仅传授理论知识，还强调实践操作，有助于读者将MATLAB的工具箱功能应用于具体工程和科研项目中。

Preface

It has been nearly 4 years since the rst edition of Numerical Methods for Engineers and

Scientists Using MATLAB

was published. During this time, most of the material in the

rst edition has been rigorously class tested, resulting in many enhancements and modi-

cations to make the new edition even more effective and user-friendly.

As in the rst edition, the primary objective of this book is to provide the reader

with a broad knowledge of the fundamentals of numerical methods utilized in various

disciplines in engineering and science. The powerful software MATLAB is introduced

at the outset and is assimilated throughout the book to perform symbolic, graphical, and

numerical tasks. The textbook, written at the junior/senior level, methodically covers a

wide array of techniques ranging from curve tting a set of data to numerically solving

initial- and boundary-value problems. Each method is accompanied by at least one fully

worked-out example, followed by either a user-dened function or a MATLAB script le.

MATLAB built-in functions are also presented for each main topic covered.

This book consists of 10 chapters. Chapter 1 presents the necessary background material

and is divided into two parts: (1) differential equations, matrix analysis, and the matrix

eigenvalue problem, and (2) computational errors, approximations, iterative methods, and

rates of convergence.

Chapter 2 gives an in-depth introduction to the essentials of MATLAB as related

to numerical methods. The chapter addresses fundamental features such as built-in

functionsand commands, formatting options, vector and matrix operations, program ow

control, symbolic operations, and plotting capabilities. The reader also learns how to write

a user-dened function or a MATLAB script le to perform specic tasks.

Chapters 3 and 4 introduce numerical methods for solving equations. Chapter 3 focuses

on nding roots of equations of a single variable, while Chapter 4 covers methods for

solving linear and nonlinear systems of equations.

Chapter 5 is completely devoted to curve tting and interpolation techniques, includ-

ing the fast Fourier transform (FFT). Chapter 6 covers numerical differentiation and

integrationmethods. Chapters 7 and 8 present numerical methods for solving initial-value

problems and boundary-value problems, respectively.

Chapter 9 covers the numerical solution of the matrix eigenvalue problem, which entails

techniques to approximate a few or all eigenvalues of a matrix.

Chapter 10 presents numerical methods for solving elliptic, parabolic, and hyperbolic

partial differential equations, specically those that frequently arise in engineering and

science.

Pedagogy of the Book

The book is written in a user-friendly fashion that intends to make the material easy to

follow and understand by the reader. The topics are presented systematically using the

following format:

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