Assuming no prior background in linear algebra or real analysis, An Introduction to MATLAB© Programming and Numerical Methods for Engineers enables you to develop good computational problem solving techniques through the use of numerical methods and the MATLAB© programming environment. Part One introduces fundamental programming concepts, using simple examples to put new concepts quickly into practice. Part Two covers the fundamentals of algorithms and numerical analysis at a level allowing you to quickly apply results in practical settings. - Tips, warnings, and 'try this' features within each chapter help the reader develop good programming practices - Chapter summaries, key terms, and functions and operators lists at the end of each chapter allow for quick access to important information - At least three different types of end of chapter exercises - thinking, writing, and coding - let you assess your understanding and practice what you've learned
Alexandre Bayen is the Liao-Cho Professor of Engineering at UC Berkeley. He is a Professor of Electrical Engineering and Computer Science, and Civil and Environmental Engineering. He is currently the Director of the Institute of Transportation Studies (ITS). He is also a Faculty Scientist in Mechanical Engineering, at the Lawrence Berkeley National Laboratory (LBNL). He received the Engineering Degree in applied mathematics from the Ecole Polytechnique, France, in 1998, the M.S. and Ph.D. in aeronautics and astronautics from Stanford University in 1998 and 1999 respectively. He was a Visiting Researcher at NASA Ames Research Center from 2000 to 2003. Between January 2004 and December 2004, he worked as the Research Director of the Autonomous Navigation Laboratory at the Laboratoire de Recherches Balistiques et Aerodynamiques, (Ministere de la Defense, Vernon, France), where he holds the rank of Major. He has been on the faculty at UC Berkeley since 2005. Bayen has authored two books and over 200 articles in peer reviewed journals and conferences. He is the recipient of the Ballhaus Award from Stanford University, 2004, of the CAREER award from the National Science Foundation, 2009 and he is a NASA Top 10 Innovators on Water Sustainability, 2010. His projects Mobile Century and Mobile Millennium received the 2008 Best of ITS Award for 'Best Innovative Practice', at the ITS World Congress and a TRANNY Award from the California Transportation Foundation, 2009. Mobile Millennium has been featured more than 200 times in the media, including TV channels and radio stations (CBS, NBC, ABC, CNET, NPR, KGO, the BBC), and in the popular press (Wall Street Journal, Washington Post, LA Times). Bayen is the recipient of the Presidential Early Career Award for Scientists and Engineers (PECASE) award from the White House, 2010. He is also the recipient of the Okawa Research Grant Award, the Ruberti Prize from the IEEE, and the Huber Prize from the ASCE.
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List of Figures
| Fig. 1.1 | The MATLAB environment. | 4 |
| Fig. 1.2 | Truth tables for the logical AND and OR. | 10 |
| Fig. 1.3 | XOR Truth table. | 14 |
| Fig. 3.1 | The MATLAB editor. | 45 |
| Fig. 3.2 | The MATLAB path editor. | 54 |
| Fig. 5.1 | Histogram may look slightly different based on your computer. | 93 |
| Fig. 6.1 | Recursion tree for myRecFactorial(3). | 97 |
| Fig. 6.2 | Recursion Tree for myRecFib(5). | 98 |
| Fig. 6.3 | Illustration of the Towers of Hanoi. | 102 |
| Fig. 6.4 | Breakdown of one iteration of the recursive solution of the Towers of Hanoi problem. | 102 |
| Fig. 7.1 | Profiler overall results. | 118 |
| Fig. 7.2 | Profiler results for ProfilerTest.m. | 118 |
| Fig. 7.3 | Improved profiler results for ProfilerTest.m. | 120 |
| Fig. 8.1 | Various representations of the number 13. | 123 |
| Fig. 9.1 | Breakpoint inserted at line 8. | 141 |
| Fig. 9.2 | MATLAB stopped at breakpoint at line 8. | 142 |
| Fig. 10.1 | File test.txt opened in wordpad for PC. | 147 |
| Fig. 10.2 | File from previous example, test.xls, opened in Microsoft Excel. | 149 |
| Fig. 11.1 | Example of plot (x,y) where x and y are vectors. | 152 |
| Fig. 11.2 | Example of plot of the function () = 2 on the interval [-5, 5]. | 152 |
| Fig. 11.3 | Example of plot of the parabola () = 2 with a green dashed line style. | 154 |
| Fig. 11.4 | Other examples of plotting styles, illustrated for () = 2 and () = 3, respectively. | 154 |
| Fig. 11.5 | Example of use of title, xlabel, and ylabel to annotate Figure 11.4. | 155 |
| Fig. 11.6 | Example of using sprintf to create a data-specific title for a figure. | 156 |
| Fig. 11.7 | Example of using legend to create a legend within a figure. | 157 |
| Fig. 11.8 | Example of customization of a plot by using the axis command to define the size of the display window and using grid on to display a grid. | 158 |
| Fig. 11.9 | Example of plots respectively obtained with the commands plot, scatter, bar, loglog, and semilogx organized using the subplot command. | 160 |
| Fig. 11.10 | Example of a three-dimensional plot obtained for the helix ((), (), ) using plot3. | 161 |
| Fig. 11.11 | Illustration of surface and contour plots. | 163 |
| Fig. 11.12 | Snapshot from the animation obtained by execution of the code above. | 165 |
| Fig. 11.13 | Test case for problem.m7 (plotting a polygon with 5 faces). | 168 |
| Fig. 11.14 | Test case for the function myFunPlotter (f,x) on the function +exp(sin(x)). | 169 |
| Fig. 11.15 | Test case for the function myPolyPlotter (n,x) used for five polynomials () = 1 for = 1, … , 5. | 170 |
| Fig. 11.16 | Test case for the function mySierpinski (n). | 170 |
| Fig. 11.17 | Test case for the function myFern (n) with 100 iterations. | 171 |
| Fig. 11.18 | Test case for myParametricPlotter. | 172 |
| Fig. 11.19 | Test cases for mySurfacePlotter. | 173 |
| Fig. 12.1 | Illustration of the process for finding the solution to a linear system. | 189 |
| Fig. 13.1 | Results from force-displacement experiment for spring (fictional). | 202 |
| Fig. 13.2 | Illustration of the 2 projection of on the range of . | 204 |
| Fig. 13.3 | Estimation data and regression curve ˆ(x)=a1x+a2. | 207 |
| Fig. 14.1 | Illustration of the interpolation problem: estimate the value of a function in between data points. | 212 |
| Fig. 14.2 | Linear interpolation of the points = (0, 1, 2) and = (1, 3, 2). | 212 |
| Fig. 14.3 | Illustration of cubic spline interpolation. | 213 |
| Fig. 14.4 | Resulting plot of previous code. Cubic spline interpolation of the points = (0, 1, 2) and = (1, 3, 2). | 214 |
| Fig. 14.5 | Lagrange basis polynomials for test data. By design, () = 1 when = , and () = 0 when ? . | 217 |
| Fig. 14.6 | The Lagrange polynomials going through each of the data points. | 218 |
| Fig. 15.1 | Successive orders of approximation of the sin function by its Taylor expansion. | 227 |
| Fig. 15.2 | Successive levels of zoom of a smooth function to illustrate the linear nature of functions locally. | 229 |
| Fig. 16.1 | Illustration of intermediate value theorem. If sign(()) ? sign(()), then ? ? ( ) such that () = 0. | 235 |
| Fig. 16.2 | Illustration of the bisection method. | 236 |
| Fig. 16.3 | Illustration of Newton step for a smooth function, (). | 238 |
| Fig. 17.1 | Numerical grid used to approximate functions. | 246 |
| Fig. 17.2 | Illustration of the forward difference, the backward difference, and the central difference methods. | 248 |
| Fig. 17.3 | Comparison of the numerical evaluation of the explicit formula for the derivative of cos and of the derivative of cos obtained by the forward difference formula. | 250 |
| Fig. 17.4 | Maximum error between the numerical evaluation of the explicit formula for the derivative of cos and the derivative of cos obtained by forward finite differencing. | 251 |
| Fig. 17.5 | Cosine wave contaminated with a small amount of noise. The noise is hardly visible, but it will be shown that it has drastic consequences for the derivative. | 253 |
| Fig. 17.6 | Noise in numerical derivatives. | 253 |
| Fig. 18.1 | Illustration of the integral. | 260 |
| Fig. 18.2 | Illustration of the trapezoid integral procedure. | 263 |
| Fig. 18.3 | Illustration of the Simpson integral formula. | 266 |
| Fig. 18.4 | Illustration of the accounting procedure to approximate the function by the Simpson rule for the entire interval [ ]. | 267 |
| Fig. 18.5 | Illustration of a primitive of the function sin computed numerically in the interval [0 ] using the cumtrapz function. | 271 |
| Fig. 19.1 | Pendulum system. | 278 |
| Fig. 19.2 | Comparison of the approximate integration of the function (t)dt=e-t between 0 and 1 (dashed) and the exact integration (solid) using Euler’s Explicit Formula. | 283 |
| Fig. 19.3 | Comparison of the approximate integration of... |
