## Mathematical ModelingMathematical Modeling 3e is a general introduction to an increasingly crucial topic for today's mathematicians. Unlike textbooks focused on one kind of mathematical model, this book covers the broad spectrum of modeling problems, from optimization to dynamical systems to stochastic processes. Mathematical modeling is the link between mathematics and the rest of the world. Meerschaert shows how to refine a question, phrasing it in precise mathematical terms. Then he encourages students to reverse the process, translating the mathematical solution back into a comprehensible, useful answer to the original question. This textbook mirrors the process professionals must follow in solving complex problems. Each chapter in this book is followed by a set of challenging exercises. These exercises require significant effort on the part of the student, as well as a certain amount of creativity. Meerschaert did not invent the problems in this book--they are real problems, not designed to illustrate the use of any particular mathematical technique. Meerschaert's emphasis on principles and general techniques offers students the mathematical background they need to model problems in a wide range of disciplines. This new edition will be accompanied by expanded and enhanced on-line support for instructors. MATLAB material will be added to complement existing support for Maple, Mathematica, and other software packages, and the solutions manual will be provided both in hard copy and on the web. * Increased support for instructors, including MATLAB material as well as other on-line resources * New sections on time series analysis and diffusion models * Additional problems with international focus such as whale and dolphin populations, plus updated optimization problems |

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### Contents

ONE VARIABLE OPTIMIZATION | 3 |

12 Sensitivity Analysis | 9 |

13 Sensitivity and Robustness | 13 |

14 Exercises | 15 |

MULTIVARIABLE OPTIMIZATION | 19 |

22 Lagrange Multipliers | 29 |

23 Sensitivity Analysis and Shadow Prices | 39 |

24 Exercises | 48 |

62 ContinuousTime Models | 176 |

63 The Euler Method | 179 |

64 Chaos and Fractals | 191 |

65 Exercises | 204 |

PROBABILITY MODELS | 219 |

INTRODUCTION TO PROBABILITY MODELS | 221 |

72 Continuous Probability Models | 226 |

73 Introduction to Statistics | 229 |

COMPUTATIONAL METHODS FOR OPTIMIZATION | 55 |

32 Multivariable Optimization | 64 |

33 Linear Programming | 72 |

34 Discrete Optimization | 89 |

35 Exercises | 100 |

DYNAMIC MODELS | 111 |

INTRODUCTION TO DYNAMIC MODELS | 113 |

42 Dynamical Systems | 118 |

43 Discrete Time Dynamical Systems | 124 |

44 Exercises | 130 |

ANALYSIS OF DYNAMIC MODELS | 137 |

52 Eigenvalue Methods for Discrete Systems | 142 |

53 Phase Portraits | 147 |

54 Exercises | 162 |

SIMULATION OF DYNAMIC MODELS | 169 |

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### Common terms and phrases

19-inch sets algorithm approximation assume assumptions behavior blue whales calculate Chapter CM1 index color TV problem complete phase portrait computer algebra system consider constraint cost cubic yards decision variables denote Determine differential equations diodes distribution docking problem dynamic models dynamical system eigenvalues equilibrium point estimate Euler method Examine the sensitivity Exercise feasible region Figure fin whales five-step method formulate Graph growth rate initial condition integer Lagrange multipliers linear programming linear regression linear system Markov chain Markov process maximize maximum Minitab modeling approach Monte Carlo simulation nonlinear objective function obtain optimal solution optimization problem parameter Perform a sensitivity phase portrait pig problem plot population levels predictor problem of Example profit random variable Reconsider represents results of step RLC circuit robustness sensitivity analysis shadow prices solution curve solve spreadsheet steady-state Suppose UMAP module vector field week whale problem X2 versus