View source for Course notes


====Open Textbook for this course, pdf====
'''Download the latest [http://www.math.ubc.ca/~keshet/OpenBook.pdf 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 [http://copiesmart.com/ 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====
*[[Course notes/Earth's energy balance|Earth's energy balance]]
*[[Course notes/Fitting data - least squares|Fitting data - least squares]]
*[[Course notes/Optimal foraging and other repeated processes|Optimal foraging and other repeated processes]]
*[[Course notes/Numerical integration|Numerical integration]]
*[[Course notes/Degrees or radians - why you should always use radians|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.

*[http://www.math.ubc.ca/~andrewr/maths100180/2016/CLP/clp_100180.html 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.

*[http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx Paul's online notes], written by [http://www.math.lamar.edu/faculty/dawkins/dawkins.aspx Prof. Paul Dawkins] at [http://www.lamar.edu/ Lamar University] provides a good, free and online resource for a standard calculus course.
<!--====The latest version of the Math 102 Course Notes:====

*[{{ChapterLink|1}} Chapter 1]: Power functions as building blocks 
*[{{ChapterLink|2}} Chapter 2]: Average rates of change, average velocity and the secant line 
*[{{ChapterLink|3}} Chapter 3]: Three faces of the derivative: geometric, analytic, and computational 
*[{{ChapterLink|4}} Chapter 4]: Differentiation rules, simple antiderivatives and applications 
*[{{ChapterLink|5}} Chapter 5]: Tangent lines, linear approximation, and Newton’s method 
*[{{ChapterLink|6}} Chapter 6]: Sketching the graph of a function using calculus tools 
*[{{ChapterLink|7}} Chapter 7]: Optimization
*[{{ChapterLink|8}} Chapter 8]: Introducing the chain rule 
*[{{ChapterLink|9}} Chapter 9]: Chain rule applied to related rates and implicit differentiation 
*[{{ChapterLink|10}} Chapter 10]: Exponential functions 
*[{{ChapterLink|11}} Chapter 11]: Differential equations for exponential growth and decay 
*[{{ChapterLink|12}} Chapter 12]: Solving differential equations 
*[{{ChapterLink|13}} Chapter 13]: Qualitative methods for differential equations 
*[{{ChapterLink|14}} Chapter 14]: Periodic and trigonometric functions 
*[{{ChapterLink|15}} Chapter 15]: Cycles, periods, and rates of change 
*[{{ChapterLink|16}} Chapter 16]: Review Problems 
*[{{ChapterLink|appendix}} Review Problems, Appendices, Table of Contents, Answers and Index]
*[{{ChapterLink|ToC}} Table of contents]
*[{{ChapterLink|answers}} Answers]

*[{{ChapterLink|index}}| 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.'''
*[{{ChapterLink|full}} 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 $2\pi$.-->

<!--
(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 \(e^8.2\))
* Chap 14, Section 14.3: The domain and range of the inverse sine and cosine functions should be closed intervals (not open as stated in several places in this section).
-->