What Every Engineer Should Know about MATLAB« and Simulink«

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ISBN: 9781439810200 | 1439810206
Cover: Nonspecific Binding
Copyright: 7/20/2010

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Using examples from mathematics, mechanical and electrical engineering, and control and signal processing, this book provides an introduction to MATLAB Â® and Simulink and examines the advantages and limitations of both. The author demonstrates how to visualize the results of calculations in various kinds of graphical representations, how to write useful script files and functions for solving specific problems, how to avoid disastrous, computational errors, and how to insert calculations and graphs into technical reports produced by either MS Word or LaTeX. Companion software with functions and script files is available online.

Preface	p. xv
Introducing MATLAB®	p. 1
Introduction to MATLAB®	p. 3
Starting MATLAB	p. 3
Using MATLAB as a simple calculator	p. 5
How to quit MATLAB	p. 9
Using MATLAB as a scientific calculator	p. 10
Trigonometric functions	p. 10
Inverse trigonometric functions	p. 13
Other elementary functions	p. 15
Arrays of numbers	p. 16
Using MATLAB for plotting	p. 18
Annotating a graph	p. 20
Format	p. 21
Arrays of numbers	p. 22
Array elements	p. 22
Plotting resolution	p. 23
Array operations	p. 24
Writing simple functions in MATLAB	p. 27
Summary	p. 31
Examples	p. 34
More exercises	p. 42
Vectors and matrices	p. 47
Vectors in geometry	p. 48
Arrays of point coordinates in the plane	p. 48
The perimeter of a polygon - for loops	p. 52
Vectorization	p. 55
Arrays of point coordinates in solid geometry	p. 56
Geometrical interpretation of vectors	p. 61
Operating with vectors	p. 63
Vector basis	p. 65
The scalar product	p. 66
Vectors in mechanics	p. 69
Forces. The resultant of two or more forces	p. 69
Work as a scalar product	p. 72
Velocities. Composition of velocities	p. 72
Matrices	p. 73
Introduction - the matrix product	p. 73
Determinants	p. 77
Matrices in geometry	p. 78
The vector product. Parallelogram area	p. 78
The scalar triple product. Parallelepiped volume	p. 80
Transformations	p. 82
Translation - Matrix addition and subtraction	p. 82
Rotation	p. 83
Homogeneous coordinates	p. 84
Matrices in Mechanics	p. 88
Angular velocity	p. 88
Center of mass	p. 89
Moments as vector products	p. 91
Summary	p. 93
More exercises	p. 98
Equations	p. 103
Introduction	p. 103
Linear equations in geometry	p. 103
The intersection of two lines	p. 103
Cramer's rule	p. 104
MATLAB's solution of linear equations	p. 105
An example of an ill-conditioned system	p. 107
The intersection of three planes	p. 109
Linear equations in statics	p. 109
A simple beam	p. 109
Linear equations in electricity	p. 112
A DC circuit	p. 112
The method of loop currents	p. 114
On the solution of linear equations	p. 116
Homogeneous linear equations	p. 116
Overdetermined systems - least-squares solution	p. 119
Underdetermined system	p. 123
A singular system	p. 126
Another singular system	p. 128
Summary 1	p. 132
More exercises	p. 134
Polynomial equations	p. 135
MATLAB representation of polynomials	p. 135
The MATLAB root function	p. 135
The MATLAB function conv	p. 137
Iterative solution of equations	p. 143
The Newton-Raphson method	p. 143
Solving an equation with the command fzero	p. 147
Summary 2	p. 148
More exercises	p. 149
Processing and publishing the results	p. 151
Copy and paste	p. 151
Diary	p. 152
Exporting and processing figures	p. 152
Interpolation	p. 153
Interactive plotting and curve fitting	p. 153
The MATLAB® spline function	p. 157
Importing data from Excel® - histograms	p. 165
Summary	p. 167
Exercises	p. 169
Programming in MATLAB®	p. 171
Some facts about numerical computing	p. 173
Introduction	p. 173
Computer-aided mistakes	p. 174
A loop that does not stop	p. 175
Errors in trigonometric functions	p. 176
An unexpected root	p. 176
Other unexpected roots	p. 178
Accumulating errors	p. 179
Computer representation of numbers	p. 180
The set of computer numbers	p. 184
Roundoff	p. 186
Roundoff errors	p. 187
Computer arithmetic	p. 191
Why the examples in Section 5.2 failed	p. 193
Absorbtion	p. 193
Correcting a non-terminating loop	p. 194
Second-degree equation	p. 194
Unexpected polynomial roots	p. 196
Truncation error	p. 199
Complexity	p. 202
Definition, examples	p. 202
Horner's scheme	p. 205
Problems that cannot be solved	p. 206
Summary	p. 208
More examples	p. 209
More exercises	p. 211
Data types and object-oriented programming	p. 215
Structures	p. 216
Where structures can help	p. 216
Working with structures	p. 217
Cell arrays	p. 219
Classes and object-oriented programming	p. 221
What is object-oriented programming?	p. 221
Calculations with units	p. 222
Defining a class	p. 224
Defining a subclass	p. 229
Calculating with electrical units	p. 233
Summary	p. 238
Exercises	p. 240
Progressing in MATLAB®	p. 243
Complex numbers	p. 245
The introduction of complex numbers	p. 245
Complex numbers in MATLAB	p. 245
Geometric representation	p. 248
Trigonometric representation	p. 250
Exponential representation	p. 250
Functions of complex variables	p. 253
Conformal mapping	p. 255
Phasors	p. 259
Phasors	p. 259
Phasors in mechanics	p. 261
Phasors in electricity	p. 265
An application in mechanical engineering - a mechanism	p. 271
A four-link mechanism	p. 271
Displacement analysis of the four-link mechanism	p. 272
A MATLAB function that simulates the motion of the four-link mechanism	p. 274
Animation	p. 277
A variant of the function FourLink	p. 278
Summary	p. 281
Exercises	p. 283
Numerical integration	p. 287
Introduction	p. 287
The trapezoidal rule	p. 288
The formula	p. 288
The MATLAB trapz function	p. 289
Simpson's rule	p. 290
The formula	p. 290
A function that implements Simpson's rule	p. 292
The MATLAB quadl function	p. 293
Symbolic calculation of integrals	p. 295
Summary	p. 297
Exercises	p. 298
Ordinary differential equations	p. 301
Introduction	p. 301
Numerical solution of ordinary differential equations	p. 301
Cauchy form	p. 301
Numerical solution of ordinary differential equations	p. 302
Specifying the times of the solution	p. 305
Using alternative odesolvers	p. 306
Passing parameters to the model	p. 306
Alternative strategies to solve ordinary differential equations	p. 310
Runge-Kutta methods	p. 312
Predictor-corrector methods	p. 315
Stiff systems	p. 316
Conclusion: How to choose the odesolver	p. 323
Exercises	p. 324
More graphics	p. 327
Introduction	p. 327
Drawing at scale	p. 327
The cone surface and conic sections	p. 330
The cone surface	p. 330
Conic sections	p. 332
Developing the cone surface	p. 336
A helicoidal curve on the cone surface	p. 337
The listing of functions developed in this section	p. 338
GUIs - graphical user interfaces	p. 343
Summary	p. 355
Exercises	p. 356
An introduction to Simulink®	p. 359
What is simulation?	p. 359
Beats	p. 360
A model of the momentum law	p. 366
Capacitor discharge	p. 370
A mass-spring-dashpot system	p. 376
A series RLC circuit	p. 380
The pendulum	p. 383
The mathematical and the physical pendulum	p. 383
The phase plane	p. 387
Running the simulation from a script file	p. 391
Exercises	p. 393
Applications in the frequency domain	p. 395
Introduction	p. 395
Signals	p. 395
A short introduction to the DFT	p. 398
The power spectrum	p. 400
Trigonometric expansion of a signal	p. 407
High frequency signals and aliasing	p. 410
Bode plot	p. 412
Summary	p. 414
Exercises	p. 415
Answers to selected exercises	p. 417
Bibliography	p. 423
Index	p. 427
Table of Contents provided by Ingram. All Rights Reserved.

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What Every Engineer Should Know about MATLAB« and Simulink«

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