## Mathematical Explorations with MATLABThis 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. |

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### Contents

III | 3 |

IV | 6 |

V | 9 |

VI | 15 |

VII | 16 |

VIII | 18 |

IX | 23 |

X | 24 |

LXVIII | 185 |

LXX | 188 |

LXXI | 189 |

LXXII | 190 |

LXXIII | 191 |

LXXV | 196 |

LXXVI | 199 |

LXXVII | 203 |

XI | 27 |

XII | 31 |

XIII | 33 |

XIV | 34 |

XV | 36 |

XVI | 39 |

XVII | 41 |

XVIII | 44 |

XIX | 45 |

XX | 47 |

XXI | 49 |

XXII | 50 |

XXIII | 51 |

XXIV | 54 |

XXV | 58 |

XXVI | 60 |

XXVII | 63 |

XXVIII | 70 |

XXIX | 71 |

XXX | 75 |

XXXI | 76 |

XXXII | 78 |

XXXIV | 79 |

XXXV | 82 |

XXXVI | 84 |

XXXVII | 88 |

XXXVIII | 91 |

XXXIX | 94 |

XL | 96 |

XLI | 99 |

XLII | 101 |

XLIII | 102 |

XLV | 105 |

XLVI | 107 |

XLVII | 108 |

XLVIII | 111 |

XLIX | 116 |

L | 119 |

LI | 122 |

LII | 128 |

LIII | 135 |

LIV | 146 |

LV | 148 |

LVI | 149 |

LVII | 153 |

LVIII | 156 |

LIX | 159 |

LX | 164 |

LXI | 165 |

LXII | 166 |

LXIII | 168 |

LXIV | 171 |

LXV | 177 |

LXVII | 179 |

LXXVIII | 207 |

LXXIX | 208 |

LXXX | 209 |

LXXXI | 212 |

LXXXII | 213 |

LXXXIII | 214 |

LXXXIV | 217 |

LXXXV | 221 |

LXXXVI | 222 |

LXXXVII | 223 |

LXXXVIII | 224 |

LXXXIX | 227 |

XC | 228 |

XCI | 229 |

XCIII | 233 |

XCIV | 234 |

XCVI | 236 |

XCVII | 239 |

XCVIII | 240 |

XCIX | 243 |

C | 245 |

CI | 246 |

CII | 250 |

CIII | 251 |

CIV | 253 |

CV | 257 |

CVI | 258 |

CVIII | 261 |

CIX | 262 |

CX | 263 |

CXI | 265 |

CXII | 266 |

CXIII | 267 |

CXIV | 268 |

CXV | 269 |

CXVI | 271 |

CXVII | 273 |

CXVIII | 274 |

CXIX | 275 |

CXX | 277 |

CXXI | 278 |

CXXII | 281 |

CXXIII | 282 |

CXXV | 284 |

CXXVII | 285 |

CXXVIII | 286 |

CXXIX | 290 |

CXXX | 292 |

CXXXI | 296 |

CXXXII | 297 |

299 | |

301 | |

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### Common terms and phrases

approximation arrival basins of attraction calculate called cards Chapter circle cobweb diagrams coefficient column vector complex numbers contour plot convergence cubic curve cycloid data sets differential equations disjoint cycles draw eigenvalues eigenvector envelope epicycloid estimate example Exercise exponential sequences Figure fish fixed points formula full_new.m function given gives graph Hint identity matrix input integer inter-arrival investigate iterations least squares Leslie matrix linear loop M-file magic squares Mathematical ideas MATLAB command MATLAB techniques matrix mean method Miller's test Mobius sequence Note obtain out-shuffles parabola parameters parametrisation permutation matrices piecewise polynomial prime produces pseudoprimes quadratic queue rand random numbers real numbers result riffle riffle shuffle root root mean squares shuffle simple simulate snowboat solve sparse matrices spirograph starting theorem total number typing help values variables whole numbers zero zigzag