# Course notes

## Contents |

#### Open Textbook for this course, pdf

**Download the latest Full version here.**

This open book was written and is provided voluntarily by Prof. Leah Keshet (UBC Math). It is based on material she developed and taught in Math 102 over many years, and is being updated over time. It is licensed under Creative Commons, and is provided free of charge for all interested in learning. Copyrights are reserved by Keshet. Last update: September 15, 2017. (As errors/typos are found, the book will be updated. Kindly contact keshet@math.ubc.ca with typos or errors to be fixed.)

#### Open textbook updates and fixes

Sept 7: Fixed Mastered Material 19 on p 34 to avoid overlapping fig 1.5

Sept 11: Fix figure 2.6 f(b)—> f(a) corresponding to the lower point on graph

Sept 15: Fixed several typos in the Solution to Example 2.8:

- the expression c(2t0 + h) approaches 2ct0 as h shrinks to zero

- the velocity of an object at time t = 1 s after it is released is v(1) = 9.8 m/s.

Sept 16: Fixed p40 link to interactive graph to indicate P(x) = G(x)

Sept 19: Fixed the information in Exercise 1.23 (to supply the c-axis intercept)

Sept 22: p 30 “A similar strategy also allows us [to] consider” (thanks Sarah!)

Sept 26: The book now includes Short Answers to problems (up to chap 12.. more to come)

Oct 1: fixed multiple errors in Example 5.15 - Thanks Maria! Fixed the right and left limits in Appendix D4 - Thanks, Davy!

Oct 9: Replaced (wrong) figure in problem 5.18 with correct figure.

Oct 22: Corrected the labels on Fig 1.2

Nov 11: Corrected the answer to Problem 11.17. Corrected an error in the table for Example 2.4 in which Tuna 1 and Tuna 2 were switched. (Thanks Jennie!)

Nov 15: Added answers to Chapter 13-16 problems (Thanks, Fiona!)

Nov 17: Corrected the DE in Problem 11.22, Corrected the answer to Problem 11.17 (Thanks, Elyse!)

#### Hard copies

The best way to use the open course book is to download the .pdf file to your laptop or tablet. Then you can use all the internal links to interactive material. You do NOT need to buy a printed copy. This calculus "open book" is now part of the Open Textbook initiative that is meant to save you money. You can use the usual .pdf tools to highlight or annotate the file, just as you would annotate a printed copy.

You can optionally buy a printed paper copy of this material from Copiesmart on University Boulevard. The cost after tax will be $25. Be aware, though, that the printed copy will not have the full functionality of the .pdf file version.

Address: Copiesmart, #103 5728 University Blvd. Tel: 604-222-3189, 604-222-3194. Call first to see whether they are in stock, or need to have more printed. Copies should be available from the morning of Thursday Sept 6.

#### Supplements

- Earth's energy balance
- Fitting data - least squares
- Optimal foraging and other repeated processes
- Numerical integration
- Degrees or radians - why you should always use radians

#### Additional references

- Stewart's
*Calculus: Early Transcendentals*is available at the UBC bookstore and can be found secondhand as it is used for a number of other first year calculus courses on campus. It does not cover all the topics we cover in this course and covers some topics we do not cover but there is a significant overlap and, for some topics, especially the basic ones, you might find useful worked examples.

- CLP Calculus, written by several UBC faculty members, is a free online textbook with accompanying book of exercises, including hints and fully worked-out solutions.

- Paul's online notes, written by Prof. Paul Dawkins at Lamar University provides a good, free and online resource for a standard calculus course.