## Elementary Mathematical Models: Order Aplenty and a Glimpse of ChaosThe language of mathematics has proven over centuries of application to be an indispensable tool for the expression and analysis of real problems. With numerical, graphical, and theoretical methods, this book examines the relevance of mathematical models to phenomena ranging from population growth and economics to medicine and the physical sciences. In a book written for the intelligent and literate non-mathematician, Kalman aims at an understanding of the power and utility of quantitative methods rather than at technical mastery of mathematical operations. He shows first that mathematical models can serve a critical function in understanding the world, and he concludes with a discussion of the problems encountered by traditional algebraic assumptions in chaos theory. Though models can often approximate future events based on existing data and quantitative relationships, Kalman shows that the appearance of regularity and order can often be misleading. By beginning with quantitative models and ending with an introduction to chaos, Kalman offers a broad treatment of both the power and limitations of quantitatively-based predictions. |

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### Contents

Overview | 1 |

Sequences and Difference Equations | 11 |

Arithmetic Growth | 37 |

Linear Graphs Functions and Equations | 55 |

Quadratic Growth Models | 79 |

Quadratic Graphs Functions and Equations | 117 |

Polynomial and Rational Functions | 149 |

Fitting a Line to Data | 165 |

### Common terms and phrases

algebra amount an+i answer applications approximately arithmetic growth model axis base calculator carbon dioxide level chaos chapter coefficient constant curve data points data value decibel decimal difference equation pn+i discussion dose drug earlier equal error function example exponential function expressed factored form figure fish population fixed population fraction functional equation geometric growth model gives graph graphical growth factor harvest idea illustrate increase intercept kind leads linear equation linear model logarithmic scale logistic growth model logistic model look mathematical mixed model month multiplying notation numerical method oil reserves original data parameters pattern payment percent pn)pn polynomial possible predict proportional reasoning quadratic equation quadratic formula quadratic function quadratic growth models rational functions result Richter scale second differences sequence shows simple slope soda solutions solve starting population straight line strontium 90 subtracting Suppose tank total error user computers variable vertex whole number y-intercept