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## Conditions of Use

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## Table of Contents

- Functions
- Limits
- Infinity and Continuity
- Basics of Derivatives
- Curve Sketching
- The Product Rule and Quotient Rule
- The Chain Rule
- The Derivatives of Trigonometric Functions and their Inverses
- Applications of Differentiation
- Optimization
- Linear Approximation
- Antiderivatives
- Integrals
- The Fundamental Theorem of Calculus
- Techniques of Integration
- Applications of Integration

## About the Book

Calculus is about the very large, the very small, and how things change—the surprise is that something seemingly so abstract ends up explaining the real world.

This course is a first and friendly introduction to calculus, suitable for someone who has never seen the subject before, or for someone who has seen some calculus but wants to review the concepts and practice applying those concepts to solve problems. One learns calculus by doing calculus, and so this course is based around doing practice problems.

## About the Contributors

### Author(s)

**Roman Holowinsky** has been a professor in the OSU Math Department since Fall 2010. His research in the field of analytic number theory with a focus on L-functions and modular forms. Roman is an Alfred P. Sloan fellow and the recipient of the 2011 SASTRA Ramanujan prize.

**Johann Thiel** is an assistant professor at New York City College of Technology. His main research interests lie in analytic number theory and its applications. In his classes, Johann enjoys designing live demonstrations to illustrate mathematical concepts. Johann has built some of the explorations for mooculus.

**David Lindberg** is a mathematics masters student at OSU. For Calculus One, David is performing data analysis on the exercises to help improve the educational aspects of mooculus.

**Jenny George** teaches mathematics at The Ohio State University. Her research is in low-dimensional topology, which means that she gets to work with tangles and knots both in Mathematics and in her knitting. Before coming to Ohio State, she earned her undergraduate degree from Miami University, and then earned her Ph.D. at Ohio State. Jenny George is currently the head instructor for Calculus One.

**Steve Gubkin** is a mathematics Ph.D. student at OSU. Steve has extensive experience with the khan exercise framework, so for mooculus, he leads the development of our interactive exercises.

**Jim Fowler's** research broadly includes geometry and topology; specifically, his interests focus on the topology of high-dimensional manifolds and geometric group theory, which means he thinks about highly symmetric (and therefore very beautiful) geometric objects. He's fond of using computational techniques to attack problems in pure mathematics. He received an undergraduate degree from Harvard University and received a Ph.D. from the University of Chicago. Jim built the adaptive learning platform that powers mooculus.

**Bart Snapp** teaches mathematics at OSU. His research interests include commutative ring theory and recreational mathematics. He enjoys exploring connections between mathematics and real-world problems, art, and music.

**Sean Corey** teaches mathematics in secondary schools and is a proponent of independent learning. Game theory and the development of artificial intelligence are prominent interests of his. For mooculus, Sean has developed some of the interactive exercises and edited the textbook.

**Chris Bolognese** has taught mathematics both at the high school and college level. Next year he is the district teacher leader for mathematics K-12 for Upper Arlington Schools. Chris enjoys mathematics competitions and mathematical technology. For mooculus, Chris will be a teaching assistant and also contribute items for exercises.

**Tom Evans** is an Educational Technologist and the lead for open courses at the Ohio State University. You can follow him on Twitter at @taevans. For mooculus, Tom created the music and edited some of the videos.