## A Course in Mathematical ModelingThe emphasis of this book lies on the teaching of mathematical modeling rather than simply presenting models. To this end the book starts with the simple discrete exponential growth model as a building block, and successively refines it. This involves adding variable growth rates, multiple variables, fitting growth rates to data, including random elements, testing exactness of fit, using computer simulations and moving to a continuous setting. No advanced knowledge is assumed of the reader, making this book suitable for elementary modeling courses. The book can also be used to supplement courses in linear algebra, differential equations, probability theory and statistics. |

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### Contents

Discrete Dynamical Systems | 9 |

Discrete Stochasticity | 47 |

Stages States and Classes | 101 |

Empirical Modeling | 151 |

Continuous Models | 239 |

US Population Growth and Using Curves Fitted to Data | 245 |

Continuous Stochasticity | 323 |

423 | |

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age class algebra approximately arrival arrows assume assumption average number basis functions behavior box plots called carrying capacity Chapter chi-square coefficients compartmental diagram compute computer algebra system consider constant crane population curve data points data set degrees of freedom dependent variable determine difference equation differential equation discussed eigenvalue eigenvector environmental stochasticity example exponential distribution exponential model F-ratio fixed point gives graph growth rate histogram interpolation function interval linear logistic curve Markov chain Mathematica mathematical matrix multiplication mean method multiple normal distribution number of catastrophes number of viewers observed obtain occur parameters Poisson process predators predicted prey probability problem random variable recurrence relation regression line regression table sample sandhill crane shown in Figure simulation solution solve spreadsheet SSRes stability standard deviation statistics steady-state step sum of squares transition matrix values variance vector Viewers in Millions X-files zero