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E-raamat: What Every Engineer Should Know about MATLAB and Simulink

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MATLAB® can be used to execute many mathematical and engineering calculations, as well as a handheld computer canif not better. Moreover, like many other computer languages, it can perform tasks that a handheld computer cannot. Compared to other computer languages, MATLAB provides many built-in functions that make learning easier and reduce prototyping time. Simulink® is a toolbox that extends the possibilities of MATLAB by providing a graphical interface for modeling and simulating dynamical processes.

Using examples from mathematics, mechanical and electrical engineering, and control and signal processing, What Every Engineer Should Know About MATLAB® and Simulink® provides an introduction to these two computer environments and examines the advantages and limitations of MATLAB. It first explores the benefits of how to use MATLAB to solve problems and then process and present calculations and experimental results. This book also briefly introduces the reader to more advanced features of the software, such as object-oriented programming (OOP), and it draws the attention to some specialized toolboxes.

Key features of the book include demonstrations of how to:











Visualize the results of calculations in various kinds of graphical representations





Write useful script files and functions for solving specific problems





Avoid disastrous computational errors





Convert calculations into technical reports and insert calculations and graphs into either MS Word or LaTeX

This book illustrates the limitations of the computer, as well as the implications associated with errors that can result from approximations or numerical errors. Using selected examples of computer-aided errors, the author explains that the set of computer numbers is discrete and boundeda feature that can cause catastrophic errors if not properly taken into account. In conjunction with The Mathworksmarketers of MATLAB and Simulinka supplementary website is presented to offer access to software implemented in the book and the script files used to produce the figures. This book was written by Adrian B. Biran of Technion -- Israel Institute of Technology, with contributions by Moshe Breiner, managing director of SimACon.
Preface xv
I Introducing Matlab®
1(170)
1 Introduction to Matlab®
3(44)
1.1 Starting Matlab
3(2)
1.2 Using Matlab as a simple calculator
5(4)
1.3 How to quit Matlab
9(1)
1.4 Using Matlab as a scientific calculator
10(6)
1.4.1 Trigonometric functions
10(3)
1.4.2 Inverse trigonometric functions
13(2)
1.4.3 Other elementary functions
15(1)
1.5 Arrays of numbers
16(2)
1.6 Using Matlab for plotting
18(3)
1.6.1 Annotating a graph
20(1)
1.7 Format
21(1)
1.8 Arrays of numbers
22(5)
1.8.1 Array elements
22(1)
1.8.2 Plotting resolution
23(1)
1.8.3 Array operations
24(3)
1.9 Writing simple functions in Matlab
27(4)
1.10 Summary
31(3)
1.11 Examples
34(8)
1.12 More exercises
42(5)
2 Vectors and matrices
47(56)
2.1 Vectors in geometry
48(21)
2.1.1 Arrays of point coordinates in the plane
48(4)
2.1.2 The perimeter of a polygon - for loops
52(3)
2.1.3 Vectorization
55(1)
2.1.4 Arrays of point coordinates in solid geometry
56(5)
2.1.5 Geometrical interpretation of vectors
61(2)
2.1.6 Operating with vectors
63(2)
2.1.7 Vector basis
65(1)
2.1.8 The scalar product
66(3)
2.2 Vectors in mechanics
69(4)
2.2.1 Forces. The resultant of two or more forces
69(3)
2.2.2 Work as a scalar product
72(1)
2.2.3 Velocities. Composition of velocities
72(1)
2.3 Matrices
73(5)
2.3.1 Introduction - the matrix product
73(4)
2.3.2 Determinants
77(1)
2.4 Matrices in geometry
78(4)
2.4.1 The vector product. Parallelogram area
78(2)
2.4.2 The scalar triple product. Parallelepiped volume
80(2)
2.5 Transformations
82(6)
2.5.1 Translation --- Matrix addition and subtraction
82(1)
2.5.2 Rotation
83(1)
2.5.3 Homogeneous coordinates
84(4)
2.6 Matrices in Mechanics
88(5)
2.6.1 Angular velocity
88(1)
2.6.2 Center of mass
89(2)
2.6.3 Moments as vector products
91(2)
2.7 Summary
93(5)
2.8 More exercises
98(5)
3 Equations
103(48)
3.1 Introduction
103(1)
3.2 Linear equations in geometry
103(6)
3.2.1 The intersection of two lines
103(1)
3.2.2 Cramer's rule
104(1)
3.2.3 Matlab's solution of linear equations
105(2)
3.2.4 An example of an ill-conditioned system
107(2)
3.2.5 The intersection of three planes
109(1)
3.3 Linear equations in statics
109(3)
3.3.1 A simple beam
109(3)
3.4 Linear equations in electricity
112(4)
3.4.1 A DC circuit
112(2)
3.4.2 The method of loop currents
114(2)
3.5 On the solution of linear equations
116(16)
3.5.1 Homogeneous linear equations
116(3)
3.5.2 Overdetermined systems --- least-squares solution
119(4)
3.5.3 Underdetermined system
123(3)
3.5.4 A singular system
126(2)
3.5.5 Another singular system
128(4)
3.6 Summary 1
132(2)
3.7 More exercises
134(1)
3.8 Polynomial equations
135(8)
3.8.1 Matlab representation of polynomials
135(1)
3.8.2 The Matlab root function
135(2)
3.8.3 The Matlab function conv
137(6)
3.9 Iterative solution of equations
143(5)
3.9.1 The Newton-Raphson method
143(4)
3.9.2 Solving an equation with the command fzero
147(1)
3.10 Summary 2
148(1)
3.11 More exercises
149(2)
4 Processing and publishing the results
151(20)
4.1 Copy and paste
151(1)
4.2 Diary
152(1)
4.3 Exporting and processing figures
152(1)
4.4 Interpolation
153(4)
4.4.1 Interactive plotting and curve fitting
153(4)
4.5 The Matlab®spline function
157(8)
4.6 Importing data from Excel® - histograms
165(2)
4.7 Summary
167(2)
4.8 Exercises
169(2)
II Programming in Matlab®
171(72)
5 Some facts about numerical computing
173(42)
5.1 Introduction
173(1)
5.2 Computer-aided mistakes
174(6)
5.2.1 A loop that does not stop
175(1)
5.2.2 Errors in trigonometric functions
176(1)
5.2.3 An unexpected root
176(2)
5.2.4 Other unexpected roots
178(1)
5.2.5 Accumulating errors
179(1)
5.3 Computer representation of numbers
180(4)
5.4 The set of computer numbers
184(2)
5.5 Roundoff
186(1)
5.6 Roundoff errors
187(4)
5.7 Computer arithmetic
191(2)
5.8 Why the examples in Section 5.2 failed
193(6)
5.8.1 Absorbtion
193(1)
5.8.2 Correcting a non-terminating loop
194(1)
5.8.3 Second-degree equation
194(2)
5.8.4 Unexpected polynomial roots
196(3)
5.9 Truncation error
199(3)
5.10 Complexity
202(3)
5.10.1 Definition, examples
202(3)
5.11 Horner's scheme
205(1)
5.12 Problems that cannot be solved
206(2)
5.13 Summary
208(1)
5.14 More examples
209(2)
5.15 More exercises
211(4)
6 Data types and object-oriented programming
215(28)
6.1 Structures
216(3)
6.1.1 Where structures can help
216(1)
6.1.2 Working with structures
217(2)
6.2 Cell arrays
219(2)
6.3 Classes and object-oriented programming
221(17)
6.3.1 What is object-oriented programming?
221(1)
6.3.2 Calculations with units
222(2)
6.3.3 Defining a class
224(5)
6.3.4 Defining a subclass
229(4)
6.3.5 Calculating with electrical units
233(5)
6.4 Summary
238(2)
6.5 Exercises
240(3)
III Progressing in Matlab®
243(174)
7 Complex numbers
245(42)
7.1 The introduction of complex numbers
245(1)
7.2 Complex numbers in Matlab
245(3)
7.3 Geometric representation
248(2)
7.4 Trigonometric representation
250(1)
7.5 Exponential representation
250(3)
7.6 Functions of complex variables
253(2)
7.7 Conformal mapping
255(4)
7.8 Phasors
259(12)
7.8.1 Phasors
259(2)
7.8.2 Phasors in mechanics
261(4)
7.8.3 Phasors in electricity
265(6)
7.9 An application in mechanical engineering --- a mechanism
271(10)
7.9.1 A four-link mechanism
271(1)
7.9.2 Displacement analysis of the four-link mechanism
272(2)
7.9.3 A Matlab function that simulates the motion of the four-link mechanism
274(3)
7.9.4 Animation
277(1)
7.9.5 A variant of the function FourLink
278(3)
7.10 Summary
281(2)
7.11 Exercises
283(4)
8 Numerical integration
287(14)
8.1 Introduction
287(1)
8.2 The trapezoidal rule
288(2)
8.2.1 The formula
288(1)
8.2.2 The Matlab trapz function
289(1)
8.3 Simpson's rule
290(3)
8.3.1 The formula
290(2)
8.3.2 A function that implements Simpson's rule
292(1)
8.4 The Matlab quadl function
293(2)
8.5 Symbolic calculation of integrals
295(2)
8.6 Summary
297(1)
8.7 Exercises
298(3)
9 Ordinary differential equations
301(26)
9.1 Introduction
301(1)
9.2 Numerical solution of ordinary differential equations
301(1)
9.2.1 Cauchy form
301(1)
9.3 Numerical solution of ordinary differential equations
302(8)
9.3.1 Specifying the times of the solution
305(1)
9.3.2 Using alternative odesolvers
306(1)
9.3.3 Passing parameters to the model
306(4)
9.4 Alternative strategies to solve ordinary differential equations
310(13)
9.4.1 Runge---Kutta methods
312(3)
9.4.2 Predictor-corrector methods
315(1)
9.4.3 Stiff systems
316(7)
9.5 Conclusion: How to choose the odesolver
323(1)
9.6 Exercises
324(3)
10 More graphics
327(32)
10.1 Introduction
327(1)
10.2 Drawing at scale
327(3)
10.3 The cone surface and conic sections
330(13)
10.3.1 The cone surface
330(2)
10.3.2 Conic sections
332(4)
10.3.3 Developing the cone surface
336(1)
10.3.4 A helicoidal curve on the cone surface
337(1)
10.3.5 The listing of functions developed in this section
338(5)
10.4 GUIs - graphical user interfaces
343(12)
10.5 Summary
355(1)
10.6 Exercises
356(3)
11 An introduction to Simulink®
359(36)
11.1 What is simulation?
359(1)
11.2 Beats
360(6)
11.3 A model of the momentum law
366(4)
11.4 Capacitor discharge
370(6)
11.5 A mass---spring---dashpot system
376(4)
11.6 A series RLC circuit
380(3)
11.7 The pendulum
383(10)
11.7.1 The mathematical and the physical pendulum
383(4)
11.7.2 The phase plane
387(4)
11.7.3 Running the simulation from a script file
391(2)
11.8 Exercises
393(2)
12 Applications in the frequency domain
395(22)
12.1 Introduction
395(1)
12.2 Signals
395(3)
12.3 A short introduction to the DFT
398(2)
12.4 The power spectrum
400(7)
12.5 Trigonometric expansion of a signal
407(3)
12.6 High frequency signals and aliasing
410(2)
12.7 Bode plot
412(2)
12.8 Summary
414(1)
12.9 Exercises
415(2)
Answers to selected exercises 417(6)
Bibliography 423(4)
Index 427
Adrian B. Biran is on the faculty of mechanical engineering at the Technion-Israel Institute of Technology. He received his MSc and DSc from that same school, as well as a Diplomat Engineer degree from the Bucharest Polytechnic Institute. He worked extensively in design in Romania at IPRONAV-The Institute of Ship Projects, the Bucharest Studios and IPA-The Institute of Automation Projects. In Israel, he worked in design at the Israel Shipyards, and in research on Naval Architectural subjects at the Technion Research and Development Foundation. In parallel, he worked as a project instructor in Romania at the Technical Military Academy, in Israel at the Beer Sheva University (now the Ben Gurion University). Since 1972, Biran has served as an adjunct teacher in the Faculty of Mechanical Engineering of the Technion, and for the last 15 years as Adjunct Associate Professor. He has taught subjects including Machine Design, Engineering Drawing, and especially Naval Architecture. He has authored several papers on subjects such as computational linguistics and computer simulations of marine systems and subjects belonging to Ship Design. He also wrote a book on ships for popular audience and a book on Ship Hydrostatics and Stability published in English and Turkish. Together with Moshe Breiner he wrote a book on MATLAB for Engineers that was published in three English, three German, two French, and two Greek editions. Moshe Breiner graduated from the Scuola Normale di Pisa and the Universita degli Studi di Pisa and obtained a Ph.D degree from the Harvard Graduate School of Arts and Sciences. He has worked in modeling and simulations and taught MATLAB.
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