Read more about Informal Calculus with Applications to Biological and Environmental Sciences

Informal Calculus with Applications to Biological and Environmental Sciences

(2 reviews)

Tyler Seacrest, University of Montana Western

Debbie Seacrest, University of Montana Western

Rebekah Levine, University of Montana Western

Michele Anderson, University of Montana Western

Copyright Year: 2021

Publisher: TRAILS

Language: English

Formats Available

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CC BY

Reviews

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Reviewed by Theresa Allen, Senior Instructor, University of Idaho on 5/30/22

The book covers the basics well. It doesn't cover multi-variable functions, which is something we cover in our Brief Calculus at my institution, and this is the reason I rated it at a 4 instead of a 5. It has a good table of contents, but no index... read more

Reviewed by Yanping Ma, Associate Professor, Loyola Marymount University on 2/21/22

The textbook offers a review of algebra and covers all important topics of limit, derivative, and integration. The applications and modeling examples in this book, unlike the mainstream calculus textbooks, are specially designed and particularly... read more

Table of Contents

  1. Algebra Tips and Tricks: Part I
    1. Algebra Tips and Tricks Part I (Combining Terms, Distributing, Functions, Graphing)
    2. Homework for Algebra Tips and Tricks: Part I
  2. Derivative Introduction
    1. Ball Toss Project
    2. Position to Velocity
    3. Homework: Position to Velocity
    4. Algebra Tips and Tricks Part II (Piecewise Defined Functions)
    5. Limits
    6. Homework: Limits
    7. Algebra Tips and Tricks Part III (Factoring)
    8. Algebraic Limits
    9. Homework: Algebraic Limits
    10. Instantaneous Velocity
    11. Homework: Instantaneous Velocity
    12. Algebra Tips and Tricks IV (Tips for dealing with fractions)
    13. Definition of Derivative Examples
    14. Project: Hard Definition of Derivative Problems
    15. Homework: Examples of the Definition of the Derivative
    16. Project: Killdeer Migration Speed
  3. Rules for Derivatives
    1. Algebra Tips and Tricks Part V (Exponents)
    2. Power Rule
    3. Homework: Power Rule
    4. Algebra Tips and Tricks Part VI (Logarithms)
    5. Exponentials, Logarithms, and Trig Functions
    6. Homework: Exponents, Logs, Trig Functions
    7. Product Rule
    8. Homework: Product Rule
    9. Quotient Rule
    10. Homework: Quotient Rule
    11. Chain Rule
    12. Homework: Chain Rule
    13. Multirule Derivatives
    14. Homework: Multirule Derivatives
    15. Anti-derivatives
    16. Homework: Anti-derivatives
  4. More Derivative Intuition
    1. Derivatives and Graphs
    2. Homework: Derivative Graphs
    3. Second Derivatives and Interpreting the Derivative
    4. Homework: Second Derivatives and Interpreting the Derivative
    5. Optimization
    6. Homework: Optimization
    7. Derivatives in Space
    8. Homework: Derivatives in Space
  5. Differential Equations
    1. Recurrance Relations
    2. Homework: Recurrence Relations
    3. Introduction to Differential Equations
    4. Homework: Introduction to Differential Equations
    5. Understanding Differential Equations
    6. Homework: Understanding Differential Equations
    7. Initial Value Problems
    8. Homework: Initial Value Problems
    9. Growth and Decay
    10. Homework: Growth and Decay
    11. Exploring Graphs of Differential Equations
    12. Project: Modelling with Differential Equations
  6. Intuition for Integration
    1. Introduction to Integrals
    2. Numeric Integration Techniques
    3. Homework: Numeric Integration Techniques
    4. Fundamental Theorem of Calculus
    5. Homework: The Fundamental Theorem of Calculus
    6. Project: Measuring Streamflow
    7. Project: Quake Lake
  7. Rules for Integration
    1. Power, exponential, trig, and logarithm rules
    2. Homework: Power, exponential, trig, and logarithmic rules
    3. u-substitution
    4. Homework: u-substitution
    5. Integral Applications
    6. Homework: Integral Applications
    7. Integration by Parts
    8. Homework: Integration by Parts
  8. Acknowledgements

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  • About the Book

    This book is an approachable introduction to calculus with applications to biology and environmental science. For example, one application in the book is determining the volume of earth moved in the 1959 earthquake that created Quake Lake. Another application uses differential equations to model various biological examples, including moose and wolf populations at Isle Royale National Park, ranavirus in amphibians, and competing species of protozoa. The text focuses on intuitive understanding of concepts, but still covers most of the algebra and calculations common in a survey of calculus course.

    About the Contributors

    Author

    Tyler Seacrest earned his B.S. in Mathematics from Harvey Mudd College, and his M.S. and Ph.D. in Mathematics from the University of Nebraska-Lincoln.  Tyler Seacrest has taught at the University of Montana Western since 2011, and enjoys working with students at all levels. For freshman and sophomore courses, he integrates hands-on activities to make mathematics more concrete, and he is interested in making mathematics research accessible to junior and senior level students. His research area is discrete mathematics, especially graph theory, a subject with a strong history of undergraduate research.

    Editors

    Debbie Seacrest, University of Montana Western

    Rebekah Levine, University of Montana Western

    Michele Anderson, University of Montana Western

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