A Guide to Scilab with Applications
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A Guide to Scilab with Applications
About the Book
This Guide to SCILAB is a comprehensive treatment of the Scilab software system. It contains brief explanations of Scilab commands, programming, and graphing capabilities. This book is intended for beginning and experienced science and mathematics students. Coverage includes Scilab commands used in courses that involve calculus, linear algebra, differential equations, and graphics with plenty of examples and applications.
About the Author
Table of Contents
Preface i
1 Scilab Basics 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Scilab System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Scilab Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Characters and Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4.1 Special Characters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4.2 Arithmetic Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.3 Logical (Boolean) Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.4 Special Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5 Built-in Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5.1 Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.6 Homework: Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2 Matrices 25
2.1 Generating Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.1.1 Generating vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1.2 Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.1.3 Creating Column Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.1.4 Concatenating Matrices and Vectors . . . . . . . . . . . . . . . . . . . . . . 32
2.1.5 Empty Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.1.6 Addressing and Subsetting Matrices . . . . . . . . . . . . . . . . . . . . . . 34
2.1.7 Building New Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2 Matrix Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.2.1 Constructing New Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.2.2 Elementwise Arithmetic Operations . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.3 Vector Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.2.4 New Matrices from Given Matrices . . . . . . . . . . . . . . . . . . . . . . . 53
2.3 Systems of Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.3.1 Basic Functions of Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.3.2 Solving Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.3.3 Eigenvalues and Eigenvectors . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.4 Homework: Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3 Programming 69
3.1 Script Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.3 Scilab time functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.4 Basic Scilab Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.4.1 Logical Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.4.2 Selection Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.4.3 Loop Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.5 Homework: Programming, Functions and Scripts . . . . . . . . . . . . . . . . . . 95
4 2-D Graphics 97
4.1 Basic 2-D (Two-dimensional) Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.1.1 Parametric and Polar Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.1.2 Combining plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.2 Advanced 2-D Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.3 Homework: 2-d curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5 3-D Curves 138
5.1 Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6 Surface Plots 148
6.0.1 Mesh and Surface Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.0.2 plot3d and fplot3d functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.0.3 Contour Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.0.4 Color Shading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.1 Surfaces in parametric form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
6.2 Solids of Revolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.3 Homework: 3d Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
7 Data Analysis and Statistics 174
7.1 Data Entry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
7.2 Data Analysis and Statistical Functions . . . . . . . . . . . . . . . . . . . . . . . . 179
7.3 Data Visualization and Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
7.3.1 Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
7.3.2 Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
7.3.3 Bar Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
7.3.4 Pie Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
8 Computational Applications 192
8.1 Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
8.1.1 Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
8.1.2 Numerical Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
8.1.3 Zeros of equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
8.2 Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
8.3 Fourier Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
8.4 Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
8.5 Homework: Applications and Differential Equations . . . . . . . . . . . . . . . . 213
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