# Calculus Volume 2

Gilbert Strang, Massachusetts Institute of Technology

Copyright Year: 2016

ISBN 13: 9781938168062

Publisher: OpenStax

Language: English

## Formats Available

## Conditions of Use

Attribution-NonCommercial-ShareAlike

CC BY-NC-SA

## Reviews

This book includes all of the standard topics covered in Calculus II. It also includes a thorough index. read more

This book includes all of the standard topics covered in Calculus II. It also includes a thorough index.

I did not see any errors and the exposition is at an appropriate level of rigor. There are a few small typos that can be reported to be corrected as well as as some errors in exercise solutions.

This is a calculus book - the contents of calculus have not changed for a while in spite of the commercial books' practices of updating their books every year. The contents of this book are relevant and will last without changes.

Overall, it’s well written. It uses clear language and technical terminology where necessary. All new terms are defined previously.

The exposition is consistent throughout. Notation and terminology is also consistent.

The division in sections and subsections is very natural. It makes it easy to create ancillary materials for particular sections of the text.

The organization is very standard and follows a logical flow.

I used mostly the web interface, as most of my students do, and found no issues. Everything - text, figures, charts, hyperlinks - display correctly. It has a general look that could be improved if this were designed originally in LaTeX.

I did not find any grammatical errors.

I did not find any offensive or insensitive language in this book.

I strongly recommend this resource.

This is a book superior to most commercial books, in all categories. If something, it has the same problem as its commercial counterparts: is written in an editor not designed for mathematics. Both text and figures (especially figures!) would benefit from some LaTeX based editor. Also, instead of links to the commercial middle school desmos, this book would benefit from integrating an open source, higher education mathematical software like SageMath.

This is pretty much the same material as Stewart. It's very standard, very old material. read more

This is pretty much the same material as Stewart. It's very standard, very old material.

There were a few typos in the version I used. I'm not sure if that's "accuracy." There doesn't seem to be any incorrect mathematics.

This is classic stuff. Despite Wolfram Alpha and other technology that offers integration by computer, it's still my view and I'm sure the view of most educators and professionals that understanding how and why integration works is much more important than the mechanics of integration by parts. So it will always be relevant.

It's a math textbook. Some students said they were confused at some points, but that's standard for any math course.

I did not observe any inconsistency/

Sections are nicely broken up. Not necessarily one per lecture, but broken up appropriately.

The the order of topics presented is different from Stewart. The choice is arbitrary, I suppose. This text's choice made perfect sense to me.

There was some occasional discrepancies between the pdf and the online version that caused some confusion at one point, and sometimes the students who were using the browser version complained about something. I downloaded the pdf to my ipad and the performance was unimpeachable.

I did not notice any grammatical errors.

This was a math textbook.

I liked it. I liked having the pdf on my iPad. The students feedback was mostly positive. Much cheaper alternative to Stewart. There are some typos - I kept a running list (less than 10) that I plan to submit at the end of the quarter.

## Table of Contents

Chapter 1: Integration

- 1.1 Approximating Areas
- 1.2 The Definite Integral
- 1.3 The Fundamental Theorem of Calculus
- 1.4 Integration Formulas and the Net Change Theorem
- 1.5 Substitution
- 1.6 Integrals Involving Exponential and Logarithmic Functions
- 1.7 Integrals Resulting in Inverse Trigonometric Functions

Chapter 2: Applications of Integration

- 2.1 Areas between Curves
- 2.2 Determining Volumes by Slicing
- 2.3 Volumes of Revolution: Cylindrical Shells
- 2.4 Arc Length of a Curve and Surface Area
- 2.5 Physical Applications
- 2.6 Moments and Centers of Mass
- 2.7 Integrals, Exponential Functions, and Logarithms
- 2.8 Exponential Growth and Decay
- 2.9 Calculus of the Hyperbolic Functions

Chapter 3: Techniques of Integration

- 3.1 Integration by Parts
- 3.2 Trigonometric Integrals
- 3.3 Trigonometric Substitution
- 3.4 Partial Fractions
- 3.5 Other Strategies for Integration
- 3.6 Numerical Integration
- 3.7 Improper Integrals

Chapter 4: Introduction to Differential Equations

- 4.1 Basics of Differential Equations
- 4.2 Direction Fields and Numerical Methods
- 4.3 Separable Equations
- 4.4 The Logistic Equation
- 4.5 First-order Linear Equations

Chapter 5: Sequences and Series

- 5.1 Sequences
- 5.2 Infinite Series
- 5.3 The Divergence and Integral Tests
- 5.4 Comparison Tests
- 5.5 Alternating Series
- 5.6 Ratio and Root Tests

Chapter 6: Power Series

- 6.1 Power Series and Functions
- 6.2 Properties of Power Series
- 6.3 Taylor and Maclaurin Series
- 6.4 Working with Taylor Series

Chapter 7: Parametric Equations and Polar Coordinates

- 7.1 Parametric Equations
- 7.2 Calculus of Parametric Curves
- 7.3 Polar Coordinates
- 7.4 Area and Arc Length in Polar Coordinates
- 7.5 Conic Sections

## Ancillary Material

## About the Book

*Calculus *is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.

## About the Contributors

### Author

**Gilbert Strang** was an undergraduate at MIT and a Rhodes Scholar at Balliol College, Oxford. His Ph.D. was from UCLA and since then he has taught at MIT. He has been a Sloan Fellow and a Fairchild Scholar and is a Fellow of the American Academy of Arts and Sciences. He is a Professor of Mathematics at MIT, an Honorary Fellow of Balliol College, and a member of the National Academy of Sciences.

He was the President of SIAM during 1999 and 2000, and Chair of the Joint Policy Board for Mathematics. He received the von Neumann Medal of the US Association for Computational Mechanics, and the Henrici Prize for applied analysis. The first Su Buchin Prize from the International Congress of Industrial and Applied Mathematics, and the Haimo Prize from the Mathematical Association of America, were awarded for his contributions to teaching around the world.