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Introduction to Applied Mathematics for Environmental Science

  • Textbook
  • © 2006

Overview

Authors:
  1. David F. Parkhurst

    1. Indiana University, Bloomington

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  • Is only one that shows how to apply calculus to environmental problems

  • Teaches calculus to graduate students as an everyday tool for ecology and other environmental sciences

  • Includes supplementary material: sn.pub/extras

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    Pages 1-18

  3. Derivatives and Differentiation

    Pages 19-51

  4. Integration

    Pages 52-81

  5. Ordinary Differential Equations

    Pages 82-122

  6. Further Topics in ODEs

    Pages 123-136

  7. Systems of Ordinary Differential Equations

    Pages 137-146

  8. Numerical Solution of Ordinary Differential Equations

    Pages 147-165

  9. Second-Order ODEs

    Pages 166-192

  10. Linear Algebra

    Pages 193-228

  11. Non-Linear Equations

    Pages 229-249

  12. Partial Differential Equations

    Pages 250-284

  13. Back Matter

    Pages 285-317
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Keywords

About this book

For 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.

Reviews

From the reviews:

"It … explains how basic tools of mathematical analysis can be efficiently used to study problems arising in environmental sciences. … The text shall attract non-mathematical audience by clarity of exposition which concentrates mostly on ideas and techniques … . Specifically tailored to the needs of undergraduate and graduate students in environmental sciences, this unique and skillfully written book shall help them to understand and master fundamental mathematical concepts and techniques used in the analysis of applied problems." (Yuri V. Rogovchenko, Zentralblatt MATH, Vol. 1145, 2008)

Authors and Affiliations

  • Indiana University, Bloomington

    David F. Parkhurst

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