# Active Calculus

Written by: Matthew Boelkins, David Austin and Steven Schlicker (Grand Valley State University)

Published on July 19, 2016, Active Calculus was written by a trio of professors at Grand Valley State University – Matthew Boelkins, David Austin and Steven Schlicker. The text jumps right into the subject by starting each chapter with a “preview activity” which are designed to be read and completed before class. By their own admission, the text includes very few worked examples. They instead include several activities within each section designed to lead students to connect ideas, solve problems and develop an understanding of the key concepts being presented. I believe this is an interesting approach, however, without complete examples self-study students might find this calculus textbook challenging. The authors suggest that students can use Active Calculus as a stand-alone text or as a companion text.

The PDF file contains a number of links to Java Applets that further demonstrate some of calculus’ more dynamic concepts. You can purchase a Printed Copy of Active Calculus on Amazon and might save some money over printing it yourself.

1 Understanding the Derivative
1.1 How do we measure velocity?
1.2 The notion of limit
1.3 The derivative of a function at a point
1.4 The derivative function
1.5 Interpreting, estimating, and using the derivative
1.6 The second derivative
1.7 Limits, Continuity,and Differentiability
1.8 The Tangent Line Approximation
2. Computing Derivatives
2.1 Elementary derivative rules
2.2 The sine and cosine functions
2.3 The product and quotient rules
2.4 Derivatives of other trigonometric functions
2.5 The chain rule
2.6 Derivatives of Inverse Functions
2.7 Derivatives of Functions Given Implicitly
2.8 Using Derivatives to Evaluate Limits
3 Using Derivatives
3.1 Using derivatives to identify extreme values
￼3.2 Using derivatives to describe families of functions
3.3 Global Optimization
3.4 Applied Optimization
3.5 Related Rates
4. The Definite Integral
4.1 Determining distance traveled from velocity
4.2 Riemann Sums
4.3 The Definite Integral
4.4 The Fundamental Theorem of Calculus
5. Finding Antiderivatives and Evaluating Integrals
5.1 Constructing Accurate Graphs of Antiderivatives
5.2 The Second Fundamental Theorem of Calculus
5.3 Integration by Substitution
5.4 Integration by Parts
5.5 Other Options for Finding Algebraic Antiderivatives
5.6 Numerical Integration
6. Using Definite Integrals
6.1 Using Definite Integrals to Find Area and Length
6.2 Using Definite Integrals to Find Volume
6.3 Density, Mass, and Center of Mass
6.4 Physics Applications: Work, Force, and Pressure
6.5 Improper Integrals
7. Differential Equations
7.1 An Introduction to Differential Equations
7.2 Qualitative behavior of solutions to DEs
7.3 Euler’s method
7.4 Separable differential equations
7.5 Modeling with differential equations
7.6 Population Growth and the Logistic Equation
8. Sequences and Series
8.1 Sequences
8.2 Geometric Series
8.3 Series of Real Numbers
8.4 Alternating Series
8.5 Taylor Polynomials and Taylor Series
8.6 Power Series
Appendix A: Short Table of Integrals

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Active Calculus 