MATLAB The Language of Technical Computing (Mathematics) ~ Version 7

Matrices and Linear Algebra......Page 9
Function Summary......Page 10
Creating Matrices......Page 12
Vector Products and Transpose......Page 14
Multiplying Matrices......Page 16
The Kronecker Tensor Product......Page 18
Vector and Matrix Norms......Page 19
Computational Considerations......Page 21
Square Systems......Page 23
Overdetermined Systems......Page 26
Underdetermined Systems......Page 28
Overview......Page 31
Pseudoinverses......Page 32
Cholesky Factorization......Page 36
LU Factorization......Page 38
QR Factorization......Page 39
Matrix Powers and Exponentials......Page 43
Eigenvalues......Page 47
Singular Value Decomposition......Page 51
Polynomials and Interpolation......Page 53
Polynomial Function Summary......Page 54
Polynomial Roots......Page 55
Polynomial Evaluation......Page 56
Polynomial Derivatives......Page 57
Polynomial Curve Fitting......Page 58
Partial Fraction Expansion......Page 59
Interpolation Function Summary......Page 61
One-Dimensional Interpolation......Page 62
Two-Dimensional Interpolation......Page 64
Comparing Interpolation Methods......Page 65
Interpolation and Multidimensional Arrays......Page 67
Triangulation and Interpolation of Scattered Data......Page 70
Tessellation and Interpolation of Scattered Data in Higher Dimensions......Page 78
Selected Bibliography......Page 89
Data Analysis and Statistics......Page 91
Column-Oriented Data Sets......Page 93
Function Summary......Page 97
Covariance and Correlation Coefficients......Page 100
Finite Differences......Page 101
Missing Values......Page 103
Removing Outliers......Page 105
Regression and Curve Fitting......Page 106
Polynomial Regression......Page 107
Linear-in-the-Parameters Regression......Page 108
Multiple Regression......Page 110
Polynomial Fit......Page 111
Analyzing Residuals......Page 113
Exponential Fit......Page 115
Error Bounds......Page 117
The Basic Fitting Interface......Page 118
Difference Equations and Filtering......Page 129
Function Summary......Page 132
Introduction......Page 133
Magnitude and Phase of Transformed Data......Page 137
FFT Length Versus Speed......Page 139
Function Functions......Page 141
Function Summary......Page 142
Representing Functions in MATLAB......Page 143
Plotting Mathematical Functions......Page 145
Minimizing Functions of One Variable......Page 148
Minimizing Functions of Several Variables......Page 149
Fitting a Curve to Data......Page 150
Setting Minimization Options......Page 152
Output Functions......Page 154
Finding Zeros of Functions......Page 161
Troubleshooting......Page 165
Example: Computing the Length of a Curve......Page 167
Example: Double Integration......Page 168
Providing Parameter Values Using Nested Functions......Page 170
Providing Parameter Values to Anonymous Functions......Page 171
Differential Equations......Page 173
ODE Function Summary......Page 174
Introduction to Initial Value ODE Problems......Page 177
Solvers for Explicit and Linearly Implicit ODEs......Page 179
Examples: Solving Explicit ODE Problems......Page 182
Solver for Fully Implicit ODEs......Page 187
Example: Solving a Fully Implicit ODE Problem......Page 188
Changing ODE Integration Properties......Page 189
Examples: Applying the ODE Initial Value Problem Solvers......Page 190
Questions and Answers, and Troubleshooting......Page 209
DDE Function Summary......Page 216
Introduction to Initial Value DDE Problems......Page 217
DDE Solver......Page 218
Solving DDE Problems......Page 220
Discontinuities......Page 224
Changing DDE Integration Properties......Page 227
Boundary Value Problems for ODEs......Page 236
BVP Function Summary......Page 237
Introduction to Boundary Value ODE Problems......Page 238
Boundary Value Problem Solver......Page 239
Solving BVP Problems......Page 243
Using Continuation to Make a Good Initial Guess......Page 248
Solving Singular BVPs......Page 256
Changing BVP Integration Properties......Page 260
PDE Function Summary......Page 268
Introduction to PDE Problems......Page 269
MATLAB Partial Differential Equation Solver......Page 270
Solving PDE Problems......Page 274
Changing PDE Integration Properties......Page 280
Example: Electrodynamics Problem......Page 281
Selected Bibliography......Page 287
Sparse Matrices......Page 289
Function Summary......Page 290
Sparse Matrix Storage......Page 293
Creating Sparse Matrices......Page 294
Importing Sparse Matrices from Outside MATLAB......Page 299
Information About Nonzero Elements......Page 300
Viewing Sparse Matrices Graphically......Page 302
The find Function and Sparse Matrices......Page 303
Introduction to Adjacency Matrices......Page 304
The Bucky Ball......Page 305
An Airflow Model......Page 310
Standard Mathematical Operations......Page 312
Permutation and Reordering......Page 313
Factorization......Page 317
Simultaneous Linear Equations......Page 323
Eigenvalues and Singular Values......Page 326
Selected Bibliography......Page 328
Nondouble Data Types......Page 329
Introduction......Page 330
Integer Data Types......Page 332
Largest and Smallest Values for Integer Data Types......Page 333
Integer Arithmetic......Page 334
Example — Digitized Signals......Page 336
Warnings for Integer Data Types......Page 343
Data Type single......Page 345
Single-Precision Arithmetic......Page 346
The Function eps......Page 347
Example — Writing M-Files for Different Data Types......Page 348
Largest and Smallest Numbers of Type double and single......Page 351
References......Page 352
Index......Page 355