## Introduction to Applied Mathematics for Environmental ScienceFor many years, first as a student and later as a teacher, I have ob served graduate students in ecology and other environmental sci ences who had been required as undergraduates to take calculus courses. Those courses have often emphasized how to prove theo rems about the beautiful, logical structure of calculus, but have ne glected applications. Most of the time, the students have come out of such courses with little or no appreciation of how to apply calculus in their own work. Based on these observations, I developed a course de signed in part to re-teach calculus as an everyday tool in ecology and other environmental sciences. I emphasized derivations—working with story problems (sometimes quite complex ones)—in that course, and now in this book. The present textbook has developed out of my notes for that course. Its basic purpose is to describe various types of mathemati cal structures and how they can be apphed in environmental science. Thus, linear and non-linear algebraic equations, derivatives and in tegrals, and ordinary and partial differential equations are the basic kinds of structures, or types of mathematical models, discussed. For each, the discussion follows a pattern something like this: 1. An example of the type of structure, as apphed to environmental science, is given. 2. Next, a description of the structure is presented. 3. Usually, this is followed by other examples of how the structure arises in environmental science. 4. The analytic methods of solving and learning from the structure are discussed. |

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### Contents

1 | |

Derivatives and Differentiation | 19 |

Integration | 52 |

Ordinary Differential Equations | 82 |

Further Topics in ODEs | 123 |

ODE Systems | 137 |

SecondOrder ODEs | 166 |

Linear Algebra | 193 |

### Other editions - View all

Introduction to Applied Mathematics for Environmental Science David F. Parkhurst Limited preview - 2006 |

Introduction to Applied Mathematics for Environmental Science David F. Parkhurst No preview available - 2010 |

### Common terms and phrases

algebra analytic solution apply approximate assume calculations chain rule Chapter coefﬁcient concentration consider control volume curve da_1 deﬁned deﬁnition density differential equations diffusion distance energy balance estimate Euler’s method example exercise ﬁelds ﬁgure ﬁnal ﬁnd ﬁnding ﬁnite ﬁrst ﬁsh ﬂow ﬂux function Gaussian elimination heat loss heat transfer initial condition lake linear equations Lotka-Volterra equations Maclaurin series math mathematical MATLAB matrix Note numerical values obtain ordinary differential equations partial differential equations PDEs plot polynomial population problem quadratic relationship represent result root round-off error Runge-Kutta Runge-Kutta method secant method separation of variables shown in Fig Simpson’s rule slope solve speciﬁc step stream substitute Suppose surface symbols Taylor series temperature tion tube unit check variables varies yields zero