Course notes
From UBCMATH WIKI
These course notes were written by Prof. Leah Keshet (UBC Math) and are based on material taught in Math 102 over several years. They are being updated over time. These notes are provided for all interested in learning. Copyrights are reserved by Keshet. Last update: August, 2014. (A list of known errors appears below)
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: Trigonometric functions
- Chapter 15: Cycles, periods, and rates of change
- Chapter 16: Review Problems
- Appendix
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 2 (Example 2.15, p 35) denominator of last \(\Delta t\) quotient should be (2.5-2)
- Chap 2 (Defn 2.4, p 29): For a straight line, we define the rate of change of y with respect to time t
- Chap 5 (Example 5.1, p 95): Tangent line intersects x axis at 6.75/5.75=1.174
- Chap 6 (Example 6.13): the interval should include the endpoints \(0.1 \le x \le 4\)
- Chap 8 (Example 8.1, p 160): In the solution, the two functions are reversed.
- Chap 8 (Example 8.3, p 161): $\frac{dy}{du}$ is missing a factor of 10 from the Power Rule. In the final answer, replace 5 by 50.
- Chap 10 (Example 10.8) has a bad error. The eqn of the tangent line should be y=x+1.
- Chap 10 (Example 10.15): in the solution, \(a=e^{8.2}\) (not \(e^8.2\))
Supplements
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.
