Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises.
In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface.
The student workbook: Active Calculus Single Variable Workbook for Chapters 1-4
The student workbook: Active Calculus Single Variable Workbook for Chapters 5-8
Conditions of Use
This book is licensed under a Creative Commons License (CC BY-NC-SA). You can download the ebook Active Calculus Single Variable for free.
- Title
- Active Calculus Single Variable
- Author(s)
- Matthew Boelkins
- Published
- 2018-08-13
- Edition
- 1
- Format
- eBook (pdf, epub, mobi)
- Pages
- 539
- Language
- English
- ISBN-10
- 1724458329
- ISBN-13
- 9781724458322
- License
- CC BY-NC-SA
- Book Homepage
- Free eBook, Errata, Code, Solutions, etc.
Acknowledgements Contributors Active Calculus: Our Goals Features of the Text Students! Read this! Instructors! Read this! Understanding the Derivative How do we measure velocity? The notion of limit The derivative of a function at a point The derivative function Interpreting, estimating, and using the derivative The second derivative Limits, Continuity, and Differentiability The Tangent Line Approximation Computing Derivatives Elementary derivative rules The sine and cosine functions The product and quotient rules Derivatives of other trigonometric functions The chain rule Derivatives of Inverse Functions Derivatives of Functions Given Implicitly Using Derivatives to Evaluate Limits Using Derivatives Using derivatives to identify extreme values Using derivatives to describe families of functions Global Optimization Applied Optimization Related Rates The Definite Integral Determining distance traveled from velocity Riemann Sums The Definite Integral The Fundamental Theorem of Calculus Evaluating Integrals Constructing Accurate Graphs of Antiderivatives The Second Fundamental Theorem of Calculus Integration by Substitution Integration by Parts Other Options for Finding Algebraic Antiderivatives Numerical Integration Using Definite Integrals Using Definite Integrals to Find Area and Length Using Definite Integrals to Find Volume Density, Mass, and Center of Mass Physics Applications: Work, Force, and Pressure Improper Integrals Differential Equations An Introduction to Differential Equations Qualitative behavior of solutions to DEs Euler's method Separable differential equations Modeling with differential equations Population Growth and the Logistic Equation Sequences and Series Sequences Geometric Series Series of Real Numbers Alternating Series Taylor Polynomials and Taylor Series Power Series A Short Table of Integrals Answers to Activities Answers to Selected Exercises Index
