# Calculus One

Roman Holowinsky, Columbus, Ohio

Johann Thiel, Brooklyn, New York

David Lindberg, Columbus, Ohio

Copyright Year: 2014

Publisher: Mooculus

Language: English

## Formats Available

## Conditions of Use

Attribution-NonCommercial-ShareAlike

CC BY-NC-SA

## Reviews

The review of funcitons could be more comprehensive to include trig functions, exponentials, logarithmics. There is an index, but no glossary. read more

The review of funcitons could be more comprehensive to include trig functions, exponentials, logarithmics. There is an index, but no glossary.

The content is accurate; I did not find any errors.

Man/Woman is used a lot in the application problems. It probably should be updated to person, them/they, etc.

The text is clear and concise. I really like the "Warnings" which are common mistakes made by students.

The text is consistent with the frameworks of a Calculus I course.

The text has a nice layout with fifteen chapters. Each chapter has several sections in it which can be tailored for individual instructor's needs. There is a "List of Main Theorems" index right after the "Contents" so you can easily access the big theorems.

Each chapter is laid out in a consistent manner. Definitions are highlighted in gray, theorems in blue, warnings in pink with explanations and examples following. Graphs, charts and other figures are always on the right. Practice exercises are at the end of each section.

Very easy to navigate in the PDF format. I did not see any issues as far as displaying images/figures.

I did not come accross any grammatical errors.

Aside from using man/woman in some problems I did not find this text inclusive or exclusive of any race, ehnicity, or background.

This is a great text for a Calc I course.

Sections are arranged in a reasonable order. The only thing I'd wish to have in Calc I is the exponential functions, their inverses (logs) and their derivatives. But I understand even for traditional Calc books, not all of them contain such... read more

Sections are arranged in a reasonable order. The only thing I'd wish to have in Calc I is the exponential functions, their inverses (logs) and their derivatives. But I understand even for traditional Calc books, not all of them contain such content.

I didn't see any significant errors.

Calculus I is pretty traditional by default. I like the layout: text content on one side and graphs & scratches on the other side of the paper for the aid. I am a fan of the "Warning" parts. I think beginners and benefit a lot from those.

See above

Yes, sections are contributing to the big picture nicely.

Practice problems and keys are neatly arranged! (Of course I always wish there are more challenging problems without keys.) Each section is of about the right size: good enough to have a point or two; but not too ambitious.

Yes, sections are nicely arranged. As I mentioned above, the only thing I wish to add would be calculus of e^x and ln(x).

With a PDF version, this one shall be quite interface independent.

It's all good in math language too.

Not like some Calc-I textbooks that emphasize applications in Physics, this one come across several other fields too, such as biology and economics.

The authors spent significant efforts on graphics, tips, and examples to improve user experience.

## Table of Contents

- 0 Functions
- 1 Limits
- 2 Infinity and Continuity
- 3 Basics of Derivatives
- 4 Curve Sketching
- 5 The Product Rule and Quotient Rule
- 6 The Chain Rule
- 7 The Derivatives of Trigonometric Functions and their Inverses
- 8 Applications of Differentiation
- 9 Optimization
- 10 Linear Approximation
- 11 Antiderivatives
- 12 Integrals
- 13 The Fundamental Theorem of Calculus
- 14 Techniques of Integration
- 15 Applications of Integration

## Ancillary Material

## 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

### Authors

**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.