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Informal Calculus with Applications to Biological and Environmental Sciences
- Format:
- Book
- Author/Creator:
- Seacrest, Tyler, author.
- Language:
- English
- Subjects (All):
- Mathematics--Textbooks.
- Mathematics.
- Applied mathematics--Textbooks.
- Applied mathematics.
- Physical Description:
- 1 online resource
- Place of Publication:
- [Place of publication not identified] TRAILS [2021]
- Language Note:
- In English.
- Summary:
- 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.
- Contents:
- Algebra Tips and Tricks: Part I
- Algebra Tips and Tricks Part I (Combining Terms, Distributing, Functions, Graphing)
- Homework for Algebra Tips and Tricks: Part I
- Derivative Introduction
- Ball Toss Project
- Position to Velocity
- Homework: Position to Velocity
- Algebra Tips and Tricks Part II (Piecewise Defined Functions)
- Limits
- Homework: Limits
- Algebra Tips and Tricks Part III (Factoring)
- Algebraic Limits
- Homework: Algebraic Limits
- Instantaneous Velocity
- Homework: Instantaneous Velocity
- Algebra Tips and Tricks IV (Tips for dealing with fractions)
- Definition of Derivative Examples
- Project: Hard Definition of Derivative Problems
- Homework: Examples of the Definition of the Derivative
- Project: Killdeer Migration Speed
- Rules for Derivatives
- Algebra Tips and Tricks Part V (Exponents)
- Power Rule
- Homework: Power Rule
- Algebra Tips and Tricks Part VI (Logarithms)
- Exponentials, Logarithms, and Trig Functions
- Homework: Exponents, Logs, Trig Functions
- Product Rule
- Homework: Product Rule
- Quotient Rule
- Homework: Quotient Rule
- Chain Rule
- Homework: Chain Rule
- Multirule Derivatives
- Homework: Multirule Derivatives
- Anti-derivatives
- Homework: Anti-derivatives
- More Derivative Intuition
- Derivatives and Graphs
- Homework: Derivative Graphs
- Second Derivatives and Interpreting the Derivative
- Homework: Second Derivatives and Interpreting the Derivative
- Optimization
- Homework: Optimization
- Derivatives in Space
- Homework: Derivatives in Space
- Differential Equations
- Recurrance Relations
- Homework: Recurrence Relations
- Introduction to Differential Equations
- Homework: Introduction to Differential Equations
- Understanding Differential Equations
- Homework: Understanding Differential Equations
- Initial Value Problems
- Homework: Initial Value Problems
- Growth and Decay
- Homework: Growth and Decay
- Exploring Graphs of Differential Equations
- Project: Modelling with Differential Equations
- Intuition for Integration
- Introduction to Integrals
- Numeric Integration Techniques
- Homework: Numeric Integration Techniques
- Fundamental Theorem of Calculus
- Homework: The Fundamental Theorem of Calculus
- Project: Measuring Streamflow
- Project: Quake Lake
- Rules for Integration
- Power, exponential, trig, and logarithm rules
- Homework: Power, exponential, trig, and logarithmic rules
- u-substitution
- Homework: u-substitution
- Integral Applications
- Homework: Integral Applications
- Integration by Parts
- Homework: Integration by Parts
- Acknowledgements
- Notes:
- Description based on print resource
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