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NUMERICAL METHODS FOR ENGINEERS AND SCIENTISTS AN INTRODUCTION WITH APPLICATIONS USING MATLABPDF电子书下载

外文

• 作 者：AMOS GILAT
• 出 版 社：WILEY
• 出版年份：2014
• ISBN：9781118554937
• 页数：559 页

图书介绍： 查看图书目录点击购买PDF全本电子书 上一篇：Fresh Water in International Law下一篇：XERORADIOGRPAHY BREAST CALCIFICATIONS 《NUMERICAL METHODS FOR ENGINEERS AND SCIENTISTS AN INTRODUCTION WITH APPLICATIONS USING MATLAB》目录 标签：

Chapter 1 Introduction1

1.1 Background1

1.2 Representation of Numbers on a Computer4

1.3 Errors in Numerical Solutions10

1.3.1 Round-Off Errors10

1.3.2 Truncation Errors13

1.3.3 Total Error14

1.4 Computers and Programming15

1.5 Problems18

Chapter 2 Mathematical Background23

2.1 Background23

2.2 Concepts from Pre-Calculus and Calculus24

2.3 Vectors28

2.3.1 Operations with Vectors30

2.4 Matrices and Linear Algebra32

2.4.1 Operations with Matrices33

2.4.2 Special Matrices35

2.4.3 Inverse of a Matrix36

2.4.4 Properties of Matrices37

2.4.5 Determinant of a Matrix37

2.4.6 Cramers Rule and Solution of a System of Simultaneous Linear Equations38

2.4.7 Norms40

2.5 Ordinary Differential Equations （ODE）41

2.6 Functions of Two or More Independent Variables44

2.6.1 Definition of the Partial Derivative44

2.6.2 Chain Rule45

2.6.3 The Jacobian46

2.7 Taylor Series Expansion of Functions47

2.7.1 Taylor Series for a Function of One Variable47

2.7.2 Taylor Series for a Function of Two Variables49

2.8 Inner Product and Orthogonality50

2.9 Problems51

7.5 The Discrete Fourier Series and Discrete Fourier Transform263

7.6 Complex Discrete Fourier Transform268

7.7 Power （Energy） Spectrum271

7.8 Aliasing and Nyquist Frequency272

7.9 Alternative Forms of the Discrete Fourier Transform278

7.10 Use of MATLAB Built-In Functions for Calculating Discrete Fourier Transform278

7.11 Leakage and Windowing284

7.12 Bandwidth and Filters286

7.13 The Fast Fourier Transform （FFT）289

7.14 Problems298

Chapter 8 Numerical Differentiation303

8.1 Background303

8.2 Finite Difference Approximation of the Derivative305

8.3 Finite Difference Formulas Using Taylor Series Expansion310

8.3.1 Finite Difference Formulas of First Derivative310

8.3.2 Finite Difference Formulas for the Second Derivative315

8.4 Summary of Finite Difference Formulas for Numerical Differentiation317

8.5 Differentiation Formulas Using Lagrange Polynomials319

8.6 Differentiation Using Curve Fitting320

8.7 Use of MATLAB Built-In Functions for Numerical Differentiation320

8.8 Richardson’s Extrapolation322

8.9 Error in Numerical Differentiation325

8.10 Numerical Partial Differentiation327

8.11 Problems330

Chapter 9 Numerical Integration341

9.1 Background341

9.1.1 Overview ofApproaches in Numerical Integration342

9.2 Rectangle and Midpoint Methods344

9.3 Trapezoidal Method346

9.3.1 Composite Trapezoidal Method347

9.4 Simpson’s Methods350

9.4.1 Simpsons 1/3 Method350

9.4.2 Simpsons 3/8 Method353

9.5 Gauss Quadrature355

9.6 Evaluation of Multiple Integrals360

9.7 Use of MATLAB Built-In Functions for Integration362

9.8 Estimation of Error in Numerical Integration364

9.9 Richardson’s Extrapolation366

9.10 Romberg Integration369

9.11 Improper Integrals372

9.11.1 Integrals with Singularities372

9.11.2 Integrals with Unbounded Limits373

9.12 Problems374

Chapter 10 Ordinary Differential Equations：Initial-Value Problems385

10.1 Background385

10.2 Euler’s Methods390

10.2.1 Euler’s Explicit Method390

10.2.2 Analysis of Truncation Error in Euler’s Explicit Method394

10.2.3 Eulers Implicit Method398

10.3 Modified Euler’s Method401

10.4 Midpoint Method404

10.5 Runge-Kutta Methods405

10.5.1 Second-Order Runge-Kutta Methods406

10.5.2 Third-Order Runge-Kutta Methods410

10.5.3 Fourth-Order Runge-Kutta Methods411

10.6 Multistep Methods417

10.6.1 Adams-Bashforth Method418

10.6.2 Adams-Moulton Method419

10.7 Predictor-Corrector Methods420

10.8 System of First-Order Ordinary Differential Equations422

10.8.1 Solving a System ofFirst-Order ODEs Using Eulers Explicit Method424

10.8.2 Solving a System of First-Order ODEs Using Second-Order Runge-Kutta Method （Modified Euler Version）424

10.8.3 Solving a System ofFirst-Order ODEs Using the Classical Fourth-Order Runge-Kutta Method431

10.9 Solving a Higher-Order Initial Value Problem432

10.10 Use of MATLAB Built-In Functions for Solving Initial-Value Problems437

10.10.1 Solving a Single First-Order ODE Using MATLAB438

10.10.2 Solving a System of First-Order ODEs Using MATLAB444

10.11 Local Truncation Error in Second-Order Range-Kutta Method447

10.12 Step Size for Desired Accuracy448

10.13 Stability452

10.14 Stiff Ordinary Differential Equations454

10.15 Problems457

Chapter 11 Ordinary Differential Equations：Boundary-Value Problems471

11.1 Background471

11.2 The Shooting Method474

11.3 Finite Difference Method482

11.4 Use of MATLAB Built-In Functions for Solving Boundary Value Problems492

11.5 Error and Stability in Numerical Solution of Boundary Value Problems497

11.6 Problems499

Appendix A Introductory MA TLAB509

A.1 Background509

A.2 Starting with MATLAB509

A.3 Arrays514

A.4 Mathematical Operations with Arrays519

A.5 Script Files524

A.6 Plotting526

A.7 User-Defined Functions and Function Files528

A.8 Anonymous Functions530

A.9 Function functions532

A.10 Subfunctions535

A.11 Programming in MATLAB537

A.11.1 Relational and Logical Operators537

A.11.2 Conditional Statements，if-else Structures538

A.11.3 Loops541

A.12 Problems542

Appendix B MATLAB Programs547

Appendix C Derivation of the Real Discrete Fourier Transform（DFT）551

C.1 Orthogonality of Sines and Cosines for Discrete Points551

C.2 Determination of the Real DFT553

Index555

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摘要：NUMERICAL METHODS FOR ENGINEERS AND SCIENTISTS AN INTRODUCTION WITH APPLICATIONS USING MATLAB.pdf电子书版文档下载是一本专注于工程和科学领域数值方法的入门级教材。本书以MATLAB为工具，通过丰富的实例和实际应用，深入浅出地介绍了数值方法的基本原理和操作技巧，旨在帮助读者掌握数值方法在工程和科学研究中的应用。

1、内容概述

NUMERICAL METHODS FOR ENGINEERS AND SCIENTISTS AN INTRODUCTION WITH APPLICATIONS USING MATLAB.pdf电子书版文档下载共分为12章，涵盖了数值方法的基本概念、常用算法以及MATLAB编程技巧。从数值微分和积分、线性方程组求解到数值优化、数值积分和数值微分方程，本书系统地介绍了数值方法在各个领域的应用。

本书以实际问题为背景，通过MATLAB编程实现数值方法，使读者能够直观地理解数值方法的基本原理和操作技巧。此外，书中还提供了大量的实例和习题，帮助读者巩固所学知识。

本书内容丰富，结构清晰，适合工程和科学领域的本科生、研究生以及相关领域的科研人员阅读。

2、MATLAB应用

NUMERICAL METHODS FOR ENGINEERS AND SCIENTISTS AN INTRODUCTION WITH APPLICATIONS USING MATLAB.pdf电子书版文档下载以MATLAB为工具，通过丰富的实例展示了数值方法在实际问题中的应用。书中详细介绍了MATLAB编程技巧，使读者能够轻松地将数值方法应用于实际问题。

例如，在数值微分和积分章节，书中通过MATLAB编程实现了梯形法、辛普森法等数值积分方法，使读者能够直观地理解这些方法的基本原理和操作技巧。在数值优化章节，书中介绍了MATLAB优化工具箱的使用方法，使读者能够解决实际问题中的优化问题。

此外，书中还提供了大量的MATLAB代码示例，使读者能够快速掌握MATLAB编程技巧，提高编程能力。

3、实例分析

NUMERICAL METHODS FOR ENGINEERS AND SCIENTISTS AN INTRODUCTION WITH APPLICATIONS USING MATLAB.pdf电子书版文档下载通过大量的实例分析，使读者能够深入了解数值方法在实际问题中的应用。这些实例涵盖了工程和科学领域的多个方面，如结构分析、流体力学、电磁场等。

例如，在数值微分方程章节，书中通过实例展示了数值方法在求解非线性微分方程中的应用。在数值优化章节，书中通过实例展示了数值方法在求解实际优化问题中的应用。这些实例使读者能够将所学知识应用于实际问题，提高解决实际问题的能力。

此外，书中还提供了大量的习题，使读者能够巩固所学知识，提高解题能力。

4、总结与展望

NUMERICAL METHODS FOR ENGINEERS AND SCIENTISTS AN INTRODUCTION WITH APPLICATIONS USING MATLAB.pdf电子书版文档下载是一本优秀的数值方法教材，为读者提供了丰富的实例和实际应用。本书不仅介绍了数值方法的基本原理和操作技巧，还通过MATLAB编程展示了数值方法在实际问题中的应用。

随着科学技术的不断发展，数值方法在工程和科学研究中的应用越来越广泛。本书为读者提供了良好的学习基础，有助于读者在今后的学习和工作中更好地应用数值方法。

总结：

NUMERICAL METHODS FOR ENGINEERS AND SCIENTISTS AN INTRODUCTION WITH APPLICATIONS USING MATLAB.pdf电子书版文档下载是一本内容丰富、结构清晰、实例丰富的数值方法教材。本书以MATLAB为工具，通过丰富的实例和实际应用，深入浅出地介绍了数值方法的基本原理和操作技巧，旨在帮助读者掌握数值方法在工程和科学研究中的应用。

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