# Course notes

These course notes were written and have been provided voluntarily for many years by Prof. Leah Keshet (UBC Math). They have been based on material she developed and taught in Math 102.

You can optionally get a full printed copy of the notes at [1] Copiesmart (5728 University Blvd #103, Vancouver, BC V6T 1K6).

Or: download the Full version (see below), which has internal links from the table of contents and index.

They are being updated over time. These notes are provided for all interested in learning. Copyrights are reserved by Keshet. Last update: September, 2015. (A list of known errors appears below)

## Contents |

#### The latest version of the Math 102 Course Notes:

- Chapter 1: Power functions as building blocks
- Chapter 2: Average rates of change, average velocity and the secant line
- Chapter 3: Three faces of the derivative: geometric, analytic, and computational
- Chapter 4: Differentiation rules, simple antiderivatives and applications
- Chapter 5: Tangent lines, linear approximation, and Newton’s method
- Chapter 6: Sketching the graph of a function using calculus tools
- Chapter 7: Optimization
- Chapter 8: Introducing the chain rule
- Chapter 9: Chain rule applied to related rates and implicit differentiation
- Chapter 10: Exponential functions
- Chapter 11: Differential equations for exponential growth and decay
- Chapter 12: Solving differential equations
- Chapter 13: Qualitative methods for differential equations
- Chapter 14: Periodic and trigonometric functions
- Chapter 15: Cycles, periods, and rates of change
- Review Problems, Appendices, Table of Contents, Answers and Index

**The Full version (below) has embedded html links. Download that version to your laptop or ipad to have full capability of the internal links.**

- Full pdf version with internal links

#### Known errors in Course Notes

- Chap 1: The solution to 1.26 (a) should be 0,1.
- Chap 2: Defn 2.13: should be (change in y)/(change in x)
- last paragraph of p 10: "column" should be replaced by "row" in referring to Fig 1.4
- The solution in Example 2.11 and the graph in Figure 2.2 have swapped the data for Tuna 1 and Tuna 2.
- The y-intercept of the secant line in the solution to problem 2.7 should be -8.918 not -2.226.
- Definition of linear differential equation is confusing as independent variable/dependent variable are not clear in this context
- The graph in Figure 15.6 should start with a zero slope.
- The period of $tan(x)$ and $cot(x)$ is $T=\pi$. On page 274, the text seems to say that the period is $2\pi$.

#### 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

#### Hard copies

You can buy a printed paper copy of this material from Copiesmart on University Boulevard.

Address: Copiesmart, #103 5728 University Blvd. Tel: 604-222-3189, 604-222-3194.

#### 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.

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