Experiments with MATLAB

More documents

Recommendations

Info

$Print Preview - C:\TEMP\Adoc_86080_1404\.aptcache\ae2k0pft ...$

36 Chapter 3. Calendars and Clocks 690 689 688 687 686 685 684 683 682 681 680 Su M Tu W Th F Sa Figure 3.1. The 13th is more likely to be on Friday than any other day. c = zeros(1,7); for y = 1601:2000 for m = 1:12 d = datenum([y,m,13]); w = weekday(d); c(w) = c(w) + 1; end end c bar(c) axis([0 8 680 690]) avg = 4800/7; line([0 8], [avg avg],’linewidth’,4,’color’,’black’) set(gca,’xticklabel’,{’Su’,’M’,’Tu’,’W’,’Th’,’F’,’Sa’}) c = 687 685 685 687 684 688 684 So the 13th day of a month is more likely to be on a Friday than any other day of the week. The probability is 688/4800 = .143333. This probability is close to, but slightly larger than, 1/7 = .142857. Biorhythms Biorhythms were invented over 100 years ago and entered our popular culture in the 1960s. You can still find many Web sites today that offer to prepare personalized biorhythms, or that sell software to compute them. Biorhythms are based on the notion that three sinusoidal cycles influence our lives. The physical cycle has a
period of 23 days, the emotional cycle has a period of 28 days, and the intellectual cycle has a period of 33 days. For any individual, the cycles are initialized at birth. Figure 3.2 is my biorhythm, which begins on August 17, 1939, plotted for an eight-week period centered around the date this is being revised, July 27, 2011. It shows that I must be in pretty good shape. Today, I am near the peak of my intellectual cycle, and my physical and emotional cycles peaked on the same day less than a week ago. 100 50 birthday: 08/17/39 0 Physical −50Emotional Intellectual −100 06/29 07/06 07/13 07/20 07/27 08/03 08/10 08/17 08/24 07/27/11 Figure 3.2. My biorhythm. A search of the United States Government Patent and Trademark Office database of US patents issued between 1976 and 2010 finds 147 patents that are based upon or mention biorhythms. (There were just 113 in 2007.) The Web site is http://patft.uspto.gov The date and graphics functions in Matlab make the computation and display of biorhythms particularly convenient. The following code segment is part of our program biorhythm.m that plots a biorhythm for an eight-week period centered on the current date. t0 = datenum(’Aug. 17, 1939’) t1 = fix(now); t = (t1-28):1:(t1+28); y = 100*[sin(2*pi*(t-t0)/23) sin(2*pi*(t-t0)/28) sin(2*pi*(t-t0)/33)]; plot(t,y) You see that the time variable t is measured in days and that the trig functions take arguments measured in radians. 37
Page 1 and 2: Experiments with MATLAB Cleve Moler
Page 3 and 4: Contents Preface iii 1 Iteration 1
Page 5 and 6: Experiments with MATLAB R⃝ Copyri
Page 7 and 8: Preface Figure 1. exmgui provides a
Page 9 and 10: Preface v Better yet, enter edit ma
Page 11 and 12: Chapter 1 Iteration Iteration is a
Page 13 and 14: x = 2 x = 1.732050807568877 x = 1.6
Page 15 and 16: produce a figure that has three com
Page 17 and 18: provide brief descriptions of comma
Page 19 and 20: format compact %% Names and assignm
Page 21 and 22: Express one barn-megaparsec in teas
Page 23 and 24: 1.11 cos(x). Find the numerical sol
Page 25 and 26: 2.5 2 1.5 1 0.5 0 −0.5 −1 −1.
Page 27 and 28: Chapter 2 Fibonacci Numbers Fibonac
Page 29 and 30: f = zeros(n,1); f(1) = 1; f(2) = 2;
Page 31 and 32: The fibnum function is recursive. I
Page 33 and 34: 2.00000000000000 1.50000000000000 1
Page 35 and 36: and ends with Recap 2 3 5 8 13 21 3
Page 37 and 38: Exercises 2.1 Rabbits. Explain what
Page 39 and 40: Our function fibfun1 is a first att
Page 41 and 42: There is no array of coefficients.
Page 43 and 44: Chapter 3 Calendars and Clocks Comp
Page 45: and datenum(2011,8,2) datenum(’Au
Page 49 and 50: xmas = datenum(c(1),12,25) days_til
Page 51 and 52: 3.9 Your birthday. On which day of
Page 53 and 54: (b) Make clockex run counter-clockw
Page 55 and 56: Chapter 4 Matrices Matlab began as
Page 57 and 58: This implies that points near x are
Page 59 and 60: 10 8 6 4 2 0 −2 −4 −6 −8 3
Page 61 and 62: R = 2*rand(2,2) - 1 generates a 2-b
Page 63 and 64: 0.2588 0.9659 G45 = 0.7071 -0.7071
Page 65 and 66: Matrix arithmetic Matrix addition a
Page 67 and 68: % This is an executable program tha
Page 69 and 70: % and the complex conjugate transpo
Page 71 and 72: are mirror images of each other. 10
Page 73 and 74: Chapter 5 Linear Equations The most
Page 75 and 76: A = [3 12 1; 12 0 2; 0 2 3] Since a
Page 77 and 78: so b = 2.36 5.26 2.63 Now we do not
Page 79 and 80: Did that solution occur to you? The
Page 81 and 82: (c) (d) (e) (f) ⎛ ⎝ ⎛ ⎝ ⎛
Page 83 and 84: 5.7 Circuit. Figure 5.2 is the circ
Page 85 and 86: Chapter 6 Fractal Fern The fractal
Page 87 and 88: the point into the lower subfern on
Page 89 and 90: stop = uicontrol(’style’,’tog
Page 91 and 92: % fern % finitefern %% fern.jpg F =
Page 93 and 94: Chapter 7 Google PageRank The world
Page 95 and 96: The best way to compute PageRank in
Page 97 and 98:
alpha beta gamma delta sigma rho Fi
Page 99 and 100:
We see that alpha has a higher Page
Page 101 and 102:
0.02 0.018 0.016 0.014 0.012 0.01 0
Page 103 and 104:
Exercises 7.1 Use surfer and pagera
Page 105 and 106:
% PAGERANKPOW PageRank by power met
Page 107 and 108:
Chapter 8 Exponential Function The
Page 109 and 110:
0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55
Page 111 and 112:
The result gives us the numerical v
Page 113 and 114:
then log e(y) = t The function log
Page 115 and 116:
17 2292.02 2335.52 2339.65 18 2406.
Page 117 and 118:
Figure 8.3. Two plots of e iθ . 10
Page 119 and 120:
= s; n = n + 1; term = (t/n)*term;
Page 121 and 122:
format compact format long Explain
Page 123 and 124:
Chapter 9 T Puzzle A classic puzzle
Page 125 and 126:
Figure 9.4. The arrow and the rhomb
Page 127 and 128:
z = 3.0000 + 4.0000i r = 5 phi = 0.
Page 129 and 130:
% % puzzle_recap % edit puzzle_reca
Page 131 and 132:
9.8 Rotation. Reproduce figure 9.6.
Page 133 and 134:
Chapter 10 Magic Squares With origi
Page 135 and 136:
produces sum(diag(flipud(A))) 15 Th
Page 137 and 138:
.. image(X) colormap(map) axis imag
Page 139 and 140:
odd, n is odd. singly-even, n is di
Page 141 and 142:
M = n*A+B+1 131 produces a matrix w
Page 143 and 144:
Further Reading 133 The reasons why
Page 145 and 146:
%% Rank figure for n = 3:20 r(n) =
Page 147 and 148:
gbplot(hot) This is what TV movie c
Page 149 and 150:
for n = 3:20 r(n) = rank(magic(n));
Page 151 and 152:
Chapter 11 TicTacToe Magic Three si
Page 153 and 154:
Figure 11.4. Typical output from a
Page 155 and 156:
145 Briefly, then, the green moves
Page 157 and 158:
147 You see that 4 and 5 are on the
Page 159 and 160:
% function [i,j] = winningmove(X,p)
Page 161 and 162:
Chapter 12 Game of Life Conway’s
Page 163 and 164:
Figure 12.3. A glider gliding. Figu
Page 165 and 166:
generate index vectors that increas
Page 167 and 168:
Further Reading The Wikipedia artic
Page 169 and 170:
12.4 Glider collisions. What happen
Page 171 and 172:
R = P(:,2)./P(:,1); hist(P(:,1),30)
Page 173 and 174:
Chapter 13 Mandelbrot Set Fractals,
Page 175 and 176:
Figure 13.3. Two trajectories. z0 =
Page 177 and 178:
167 Use the up arrow and backspace
Page 179 and 180:
n = length(x); e = ones(n,1); z0 =
Page 181 and 182:
grid^2 * depth So the statement cou
Page 183 and 184:
4.0e-11,1024,2048,2) 173 Taking wid
Page 185 and 186:
Exercises 13.1 Explore. Use the man
Page 187 and 188:
Figure 13.8. Region #4. “Valley o
Page 189 and 190:
Figure 13.12. Region #8. “Nebula
Page 191 and 192:
Figure 13.16. Region #12. “Geode
Page 193 and 194:
Chapter 14 Sudoku Humans look for p
Page 195 and 196:
8 3 4 1 5 9 6 7 2 8 3 4 1 5 9 6 7 2
Page 197 and 198:
1 1 3 2 3 4 Figure 14.8. diag(1:4)
Page 199 and 200:
189 A number of operations on a Sud
Page 201 and 202:
191 The following statement creates
Page 203 and 204:
%% Disclaimer % Our Sudoku chapter
Page 205 and 206:
14.6 Try this. Try to use sudoku_as
Page 207 and 208:
H C D A A E I B F G B C A H C D A E
Page 209 and 210:
Chapter 15 Ordinary Differential Eq
Page 211 and 212:
Figure 15.2. Spacewar, the world’
Page 213 and 214:
203 two different values of the tim
Page 215 and 216:
1 0.8 0.6 0.4 0.2 0 −0.2 −0.4
Page 217 and 218:
will also produce figure 15.5. Use
Page 219 and 220:
plot(y(:,1),y(:,2),’-o’) axis s
Page 221 and 222:
15.5 Linear system Write the system
Page 223 and 224:
Chapter 16 Predator-Prey Model Mode
Page 225 and 226:
y = mu*eta*exp(k*t)./(eta*exp(k*t)
Page 227 and 228:
217 There are two tricky parts of t
Page 229 and 230:
eta = 1 mu = 20 ydot = @(t,y) k*(1-
Page 231 and 232:
Chapter 17 Orbits Dynamics of many-
Page 233 and 234:
Figure 17.1. Initial, and final, po
Page 235 and 236:
plot(x,y,’.-’) s = 2*sqrt(m); a
Page 237 and 238:
227 interface controls. In particul
Page 239 and 240:
1.5 1 0.5 0 −0.5 −1 −1.5 −1
Page 241 and 242:
1 0 −1 −1 0 1 1 0 −1 −1 0 1
Page 243 and 244:
0.3836 -0.4836 233 The three masses
Page 245 and 246:
0.3 0.2 0.1 0 −0.1 −0.2 −0.3
Page 247 and 248:
%% Snapshot of three dimensional Br
Page 249 and 250:
Exercises 239 17.1 Bouncing ball. (
Page 251 and 252:
Chapter 18 Shallow Water Equations
Page 253 and 254:
243 represents a three component ve
Page 255 and 256:
%% Create a two dimensional grid. m
Page 257 and 258:
Chapter 19 Morse Code Morse code de
Page 259 and 260:
produces a cell array that contains
Page 261 and 262:
And finally one assignment statemen
Page 263 and 264:
. . E T I A N M S U R W . . Figure
Page 265 and 266:
255 Encoding is a little more work
Page 267 and 268:
257 A computer byte is 8 bits and s
Page 269 and 270:
% publish morse_recap % % Related E
Page 271 and 272:
19.3 dash. Why didn’t I use an un
Page 273 and 274:
Chapter 20 Music What does 12√ 2
Page 275 and 276:
ange is -12:12. The statement piano
Page 277 and 278:
Figure 20.4. x = sin t, y = sin 3/2
Page 279 and 280:
269 a and b by entering values in e
Page 281 and 282:
5 1.334840 4/3 1.333333 0.0011 6 1.
Page 283 and 284:
Figure 20.10. C major fifth with eq
Page 285 and 286:
http://en.wikipedia.org/wiki/Music_
Page 287 and 288:
tfinal = 12*pi; t = 0:pi/512:tfinal
show all

Experiments with MATLAB

Create successful ePaper yourself

Delete template?

Save as template?