Mathematical Explorations With Matlab

, by K. Chen , Peter J. Giblin , A. Irving

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9780521630788 | 0521630789
Cover: Hardcover
Copyright: 5/13/1999

Rent

(Recommended)

$95.21

Term

Due

Price

Semester

Dec 13

$100.22

Quarter

Aug 16

$95.21

Short Term

Jul 16

$90.20

*This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping cart.
Buy New

Special Order: 1-2 Weeks

$136.93
eBook

Available Instantly

Online: 180 Days

Downloadable: 180 Days

$49.50

This book is about the kind of mathematics usually encountered in first year university courses. A key feature of the book is that this mathematics is explored in depth using the popular and powerful package MATLAB. The emphasis is on understanding and investigating the mathematics, and putting it into practice in a wide variety of modelling situations. In the process, the reader will gain some fluency with MATLAB, no starting knowledge of the package being assumed. The range of material is wide: matrices, whole numbers, complex numbers, geometry of curves and families of lines, data analysis, random numbers and simulations, and differential equations form the basic mathematics. This is applied to a large number of investigations and modelling problems, from sequences of real numbers to cafeteria queues, from card shuffling to models of fish growth. All extras to the standard MATLAB package are supplied on the World Wide Web.

Preface

Part one: Foundations

(98)

1 Introduction

(15)

1.1 First steps with MATLAB

(3)

1.2 Vectors and plots

(3)

1.3 Creating and editing script files

(6)

1.4 Getting hardcopy of things

(1)

Exercises

(2)

2 Matrices and Complex Numbers

(13)

2.1 Vectors and matrices

(5)

2.2 Complex numbers

(1)

2.3 Population dynamics: the Leslie matrix

(3)

Exercises

(4)

3 Whole Numbers

(13)

3.1 A loop to calculate Fibonacci numbers

(2)

3.2 A loop with conditionals: the 3n + 1 or hailstone problem

(1)

3.3 The euclidean algorithm for greatest common divisors

(2)

3.4 Fermat's theorem and the power algorithm

(3)

Exercises

(2)

3.5 Appendix

(3)

4 Graphs and Curves

(16)

4.1 Polynomials

(1)

4.2 Initial examples of drawing curves

(2)

4.3 Taylor polynomials

(2)

4.4 Approximations using the function polyfit

(1)

4.5 The goat problem

(1)

4.6 Envelopes of lines

(3)

Exercises

(4)

4.7 Appendix

(2)

5 Representation of Data

(15)

5.1 Data analysis

(3)

5.2 Least squares fitting

(7)

Exercises

(1)

5.3 Appendix

(4)

6 Probability and Random Numbers

(13)

6.1 Generating random numbers

(1)

6.2 Random integers

(2)

6.3 Simulating uniform distributions

(1)

6.4 Simulating normal distributions

(1)

6.5 Simulating negative exponential distributions

(3)

Exercises

(2)

6.6 Appendix

(4)

7 Differential and Difference Equations

(11)

7.1 Ordinary differential equations (ODEs)

(3)

7.2 Systems of differential equations

(3)

7.3 Difference equations

(2)

Exercises

(3)

Part two: Investigations

(144)

8 Magic Squares

101

(7)

8.1 Introduction

102

(1)

8.2 Magic squares size 3 X 3

102

(3)

8.3 Magic squares size 4 X 4

105

(2)

8.4 Magic squares size 5 X 5 (optional)

107

(1)

9 GCDs, Pseudoprimes and Miller's Test

108

(8)

A GCDs of random pairs and triples of numbers

108

(3)

B Pseudoprimes and Miller's test

111

(5)

10 Graphics: Curves and Envelopes

116

(12)

A Rose curves and epicycloids

116

(3)

B Envelopes

119

(3)

C Curves of constant width

122

(6)

11 Zigzags and Fast Curves

128

(18)

A Spirographs and zigzags

128

(7)

B Fast curves

135

(11)

12 Sequences of Real Numbers

146

(18)

12.1 Mobius sequences

146

(2)

12.2 Cobweb diagrams

148

(1)

12.3 Mobius functions and powers of matrices

149

(4)

A Investigation on Mobius sequences

153

(3)

B Attracting cycles

156

(3)

C Quadratic and exponential sequences; fixed points

159

(5)

13 Newton-Raphson Iteration and Fractals

164

(7)

13.1 Introduction

164

(1)

13.2 The equation z^(2) + 1 = 0

165

(1)

13.3 General quadratic equations

166

(2)

13.4 The cubic equation z^(3) - z = 0

168

(3)

14 Permutations

171

(18)

A Cycle decompositions

171

(6)

B Card shuffling

177

(1)

14.1 Introduction

177

(2)

14.2 Ins and outs

179

(6)

14.3 Cycles

185

(1)

14.4 Rough riffles (ruffles)

185

(3)

14.5 Appendix

188

(1)

15 Iterations for Nonlinear Equations

189

(18)

15.1 1D: Method 1 -- Newton-Raphson

190

(1)

15.2 1D: Method 2 -- Gauss-Jacobi

191

(1)

15.3 1D: Convergence analysis

191

(5)

15.4 2D: Iterations for nonlinear systems

196

(3)

15.5 2D: Contour plot and convergence history

199

(4)

Exercises

203

(4)

16 Matrices and Solution of Linear Systems

207

(14)

16.1 Operation counts

208

(1)

16.2 Dense linear systems

209

(3)

16.3 The iterative refinement algorithm

212

(1)

16.4 A perturbation analysis for Ax = b

213

(1)

16.5 Sparse matrices, graph ordering and permutations

214

(3)

Exercises

217

(4)

17 Function Interpolations and Approximation

221

(18)

17.1 1D: Introduction

222

(1)

17.2 The 1D example M-file intdemo1.m

223

(1)

17.3 1D data fitting

224

(3)

17.4 How accurate is my approximation?

227

(1)

17.5 Introduction to multi-variable approximation

228

(1)

17.6 The 2D M-file intdemo2.m

229

(1)

17.7 Contour plots, 3D plots and slicing

229

(4)

17.8 The `\' global method

233

(1)

17.9 The piecewise method

234

(1)

17.10 Comparison of approximations

234

(2)

Exercises

236

(3)

18 Ordinary Differential Equations

239

(4)

18.1 Strategy

239

(1)

Exercises

240

(3)

Part three: Modelling

243

(43)

19 Checkout Queues: Long or Short

245

(12)

19.1 Simulating queues

246

(4)

19.2 The motorway filling station

250

(1)

19.3 The Leo's cafeteria

251

(2)

Exercises

253

(4)

20 Fish Farming

257

(8)

20.1 Preliminary look at the problem

258

(1)

20.2 Models of fish growth

258

(3)

20.3 Designing the Leslie matrix

261

(1)

20.4 Fishing strategy

262

(1)

Exercises

263

(2)

21 Epidemics

265

(8)

21.1 Preliminary look at some data

266

(1)

21.2 The SIR model for the dynamics of an epidemic

267

(1)

21.3 Studying the behaviour analytically

268

(1)

21.4 Analysing the data

269

(2)

Exercises

271

(2)

22 Dynamics of Snowboating

273

(8)

22.1 Preliminary look at the problem

274

(1)

22.2 The equations of motion

275

(2)

22.3 Exploring the operating parameters

277

(1)

Exercises

278

(3)

23 Tides

281

(5)

23.1 Preliminary look at the tidal data

282

(1)

23.2 Fourier series and methods

282

(2)

23.3 Analysis of an electrical signal

284

(1)

23.4 Fourier analysis of the tidal data

284

(1)

Exercises

285

(1)

Appendix 1 MATLAB Command Summary

286

(4)

Appendix 2 Symbolic Calculations within MATLAB

290

(2)

Appendix 3 List of All M-files Supplied

292

(4)

Appendix 4 How to Get Solution M-files

296

(1)

Appendix 5 Selected MATLAB Resources on the Internet

297

(2)

References

299

(2)

Index

301

Please wait while the item is added to your bag...

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Mathematical Explorations With Matlab

Summary

Table of Contents

Supplemental Materials