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[基础] Solving Applied Mathematical Problems with MATLAB(文字版)

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发表于 2013-11-12 15:33:40 | 显示全部楼层 |阅读模式
[Contents
Preface xi
1 Computer Mathematics Languages — An Overview 1
1.1 Computer Solutions to Mathematics Problems . . . . . . . . 1
1.1.1 Why should we study computer mathematics language? 1
1.1.2 Analytical solutions versus numerical solutions . . . . . 4
1.1.3 Mathematics software packages: an overview . . . . . . 5
1.2 Summary of Computer Mathematics Languages . . . . . . . . 6
1.2.1 A brief historic review of MATLAB . . . . . . . . . . . 6
1.2.2 Three widely used computer mathematics languages . 7
1.2.3 Introduction to free scientific open-source softwares . . 7
1.3 Outline of the Book . . . . . . . . . . . . . . . . . . . . . . . 8
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Fundamentals of MATLAB Programming 11
2.1 Fundamentals of MATLAB Programming . . . . . . . . . . . 12
2.1.1 Variables and constants in MATLAB . . . . . . . . . . 12
2.1.2 Data structure . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.3 Basic structure of MATLAB . . . . . . . . . . . . . . . 14
2.1.4 Colon expressions and sub-matrices extraction . . . . . 15
2.2 Fundamental Mathematical Calculations . . . . . . . . . . . . 16
2.2.1 Algebraic operations of matrices . . . . . . . . . . . . . 16
2.2.2 Logic operations of matrices . . . . . . . . . . . . . . . 18
2.2.3 Relationship operations of matrices . . . . . . . . . . . 19
2.2.4 Simplifications and presentations of analytical results . 19
2.2.5 Basic number theory computations . . . . . . . . . . . 21
2.3 Flow Control Structures of MATLAB Language . . . . . . . 22
2.3.1 Loop control structures . . . . . . . . . . . . . . . . . . 22
2.3.2 Conditional control structures . . . . . . . . . . . . . . 24
2.3.3 Switch structure . . . . . . . . . . . . . . . . . . . . . . 25
2.3.4 Trial structure . . . . . . . . . . . . . . . . . . . . . . . 26
2.4 Writing and Debugging MATLAB Functions . . . . . . . . . 27
2.4.1 Basic structure of MATLAB functions . . . . . . . . . 27
2.4.2 Programming of functions with variable inputs/outputs 30
2.4.3 Inline functions and anonymous functions . . . . . . . 31
2.5 Two-Dimensional Graphics . . . . . . . . . . . . . . . . . . . 31
2.5.1 Basic statements of two-dimensional plotting . . . . . . 32
2.5.2 Other two-dimensional plotting statements . . . . . . . 34
2.5.3 Implicit function plotting and applications . . . . . . . 36

vi Solving Applied Mathematical Problems with MATLAB
2.5.4 Graphics decorations . . . . . . . . . . . . . . . . . . . 36
2.6 Three-Dimensional Graphics . . . . . . . . . . . . . . . . . . 39
2.6.1 Plotting of three-dimensional curves . . . . . . . . . . . 39
2.6.2 Plotting of three-dimensional surfaces . . . . . . . . . . 40
2.6.3 Viewpoint setting in 3D graphs . . . . . . . . . . . . . 43
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3 Calculus Problems 47
3.1 Analytical Solutions to Calculus Problems . . . . . . . . . . . 47
3.1.1 Analytical solutions to limit problems . . . . . . . . . . 48
3.1.2 Analytical solutions to derivative problems . . . . . . . 50
3.1.3 Analytical solutions to integral problems . . . . . . . . 55
3.2 Series Expansions and Series Evaluations . . . . . . . . . . . 58
3.2.1 Taylor series expansion . . . . . . . . . . . . . . . . . . 59
3.2.2 Fourier series expansion . . . . . . . . . . . . . . . . . 62
3.2.3 Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2.4 Sequence product . . . . . . . . . . . . . . . . . . . . . 67
3.3 Numerical Differentiation . . . . . . . . . . . . . . . . . . . . 67
3.3.1 Numerical differentiation algorithms . . . . . . . . . . 68
3.3.2 Central-point difference algorithm . . . . . . . . . . . . 69
3.3.3 Gradient computations of functions with two variables 71
3.4 Numerical Integration Problems . . . . . . . . . . . . . . . . 72
3.4.1 Numerical integration from given data using trapezoidal
method . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.4.2 Numerical integration of single variable functions . . . 74
3.4.3 Numerical solutions to double integrals . . . . . . . . . 77
3.4.4 Numerical solutions to triple integrals . . . . . . . . . . 79
3.5 Path Integrals and Line Integrals . . . . . . . . . . . . . . . . 80
3.5.1 Path integrals . . . . . . . . . . . . . . . . . . . . . . . 80
3.5.2 Line integrals . . . . . . . . . . . . . . . . . . . . . . . 81
3.6 Surface Integrals . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.6.1 Scalar surface integrals . . . . . . . . . . . . . . . . . . 83
3.6.2 Vector surface integrals . . . . . . . . . . . . . . . . . . 84
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4 Linear Algebra Problems 89
4.1 Inputting Special Matrices . . . . . . . . . . . . . . . . . . . 90
4.1.1 Numerical matrix input . . . . . . . . . . . . . . . . . . 90
4.1.2 Defining symbolic matrices . . . . . . . . . . . . . . . . 94
4.2 Fundamental Matrix Operations . . . . . . . . . . . . . . . . 95
4.2.1 Basic concepts and properties of matrices . . . . . . . . 95
4.2.2 Matrix inversion and generalized inverse of a matrix . 102
4.2.3 Matrix eigenvalue problems . . . . . . . . . . . . . . . 106
4.3 Fundamental Matrix Transformations . . . . . . . . . . . . . 109
4.3.1 Similarity transformations and orthogonal matrices . . 109
4.3.2 Triangular and Cholesky decompositions . . . . . . . . 111
4.3.3 Jordan transformations . . . . . . . . . . . . . . . . . . 114
4.3.4 Singular value decompositions . . . . . . . . . . . . . . 116
。。
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Solving Applied Mathematical Problems with MATLAB.part2.rar (3.66 MB, 下载次数: 1)
发表于 2014-7-27 16:08:57 | 显示全部楼层
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