Precalculus Second Edition Answers
Karri Weston
Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarterpre-calculus sequence including trigonometry. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of,and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. An emphasis is placed on modeling and interpretation, aswell as the important characteristics needed in calculus.
The second portion of the book introduces trigonometry. Trig is introduced through an integrated circle/triangle approach. Identities are introduced in the first chapter, and revisited throughout. Likewise, solving is introduced in the second chapter and revisted more extensively in the third chapter. As with thefirst part of the book, an emphasis is placed on motivating the concepts and on modeling and interpretation.
In addition to the paper homework sets, algorithmically generated online homework is available as part of a complete course shell package, whichalso includes a sample syllabus, teacher notes with lecture examples, sample quizzes and exams, printable classwork sheets and handouts, and chapter review problems. If you teach in Washington State, you can find the course shell in the WAMAP.org template course list. For those located elsewhere,you can access the course shell at MyOpenMath.com. A self-study version of the online course exercises is also available on MyOpenMath.com for students wanting to learn the material on their own, or who need a refresher.
The whole book or individual chapters are available for download below, or you can order a bound printed copy from Lulu.com or Amazon. If you are providing a link to students or a bookstore to purchase printed copies of the book, please direct them to this page. If you are an instructorand are using this book with your class, please drop us an email so we can track use and keep youupdated with changes.
Accessibility Note: The Word files contain equations in Equation Editor format, and graphs and images have alt-text in the primary text, but not the exercises. A screen reader friendly HTML version of the book can be read on LibreTexts
Note on versions: The links above will redirect you to the latest edition of the chapters. Older versions remain on the website, and can be accessed using direct links to the specific edition's file name, like 1.pdf
Note: On June 5, 2017, Edition 2.0 was released. The links below point to this, the most current version. This revision is not page number or section equivalent to the previous 1.x editions. If you are looking for the originalfirst edition (black cover), please go here
Yes. The book is well written and fun. It cuts out a ton of the ridiculous cruft that has clogged up the current crop of commercial freshman calculus texts. IIRC Gardner moderates some of the dated and sexist language.
Be aware of how this book's approach relates to the history and to currently fashionable ways of presenting calculus. It uses infinitesimals rather than limits. Both infinitesimals and limits are perfectly fine ways of introducing calculus. Historically, there were some concerns that infinitesimals were inherently inconsistent, but it turns out that that's not the case.
When teaching yourself something intellectually challenging, I would always suggest that you find multiple sources of information rather than just focusing on one book. There is a text by Keisler that is free online and introduces freshman calculus using infinitesimals, but with a bit more of the modern machinery. Compared to Thompson, it's boring and pedantic and slow and lacking in personality, but it's worth having on hand while working through Thompson. You may also be interested in my own textbook Fundamentals of Calculus, which introduces both infinitesimals and limits while focusing mainly on techniques and applications rather than foundational issues.
After giving the book another look I have to expand on my comment above and make it stronger: no, this isn't a good book for a first-time learner, and in fact I think it's a terrible choice. I looked at the second edition (not the Gardner update), but unless Gardner practically rewrote the book I don't think this matters much.
At the very beginning, derivatives are explained by simply stating that $dx$ is small and so $(dx)^2$ and higher powers are, like, really really small and they don't matter so we ignore them. I'm not being unfair either, this is the actual essence of his argument. It leads to wonderful chains of reasoning such as $y+dy=x^2+2x\cdot dx+(dx)^2$ but let's drop the small term (no, not that one...the really small one dummy) and actually $y+dy=x^2+2x\cdot dx$. As a real world example, we're told to think of $dx$ as a flea on an ox (which would bother the ox) and $(dx)^2$ as a flea on the flea (which wouldn't bother the ox). But wait, we can make that flea $dx$ as small as we wish, and a flea as small as we wish certainly wouldn't bother an ox. What's a beginning student supposed to make of this?
Thompson and anyone who has already learned calculus can make sense of it in hindsight, but how can it be viewed as anything but nonsense by a first-time reader? Some of the other books listed in comments are far better imo. I already recommended Hughes Hallet, and I can also highly recommend What is Calculus About by Sawyer and Calculus: An Intuitive and Physical Approach by Kline (in Dave L. Renfro's link).
It's really more about your sticktoitiveness than anything else, what you get out of it. I'm working on a language study right now. I have several different texts available on my shelf. And there are plusses and minuses. But really, the key thing that will determine if I prevail is if I stick to it or not. (I know several times I have not!)
I would probably advise a more standard book. But particularly one that has answers to the exercises (not worked solutions per se, just answers). You need to do your own drill and to check yourself. The intermediate review grammar I am self studying from has all the exercise answers. It's designed for usage. Not for acceptance by teacher committees that pan books with drill answers. And it sure as heck improves my understanding to see that I missed something and then check why (often figuring out my own mistake, but in a few cases, prompting a question of someone, which I keep a "parking lot" for.)
I like Granville although it is a tiny bit dry. But it uses simple words. And has short sections with minimal text (not in a proofy "intuitive to most casual observer" way but more in a KISS way). You can get one of the older editions free online in a pdf. Although really cost should not be a discriminating factor. Think of the value of your time invested. There is a huge cheap market for old books on Amazon, so just buying an old edition is a no brainer.
I also like Thomas Finney prior to about 1982 (when Thomas retired). Studied with their AP version in early 80s. [You can see the blue kaleidoscope cover of the book in the movie Stand and Deliver.] It is slightly more theoretical than Granville though, without being some baby real analysis craziness. I probably benefited some from partially working Granville first.
I also recommend to look at the Schaum's Outline. In general this sort of series is very useful for adult learners looking to review an old topic (minimal text for one thing, having answers, etc.) More of a businessman's "80-20" attitude versus the fussy complete-ism that you get from high end types on SE. Some posters here pan the series, but I think they are much more user friendly for a self studier. (And, like dieting, giving up is the key danger, so picking something user friendly is a good way to go. In that sense, the book you listed may be nice just because it is a little more amusing and so you may stick with it. You could even try an older politically incorrect version to provoke your laughs--either at or with, your choice. ;)
I have not used it, but one text I hear referred to is "Calculus for the Practical Man". Maybe also similar in being pretty gentle and marketed at self studiers and especially those who are a bit more dilettantish.
Also, get Steven Strogatz's "Infinite Powers" Book. It doesn't have any work problems. He very carefully explains many of the fundamental ideas of calculus. I was fuzzy on some of the ideas, and his book really cleared some items up. Calculus has a "tortoise and a hare", aspect to it. If you take it slowly you will learn more than if you try to race through it.
4. Summarize each section as you go through it so that you can review easily. Try to pull out general principles, understand concepts and make sure you can reconstruct the main formulas. Make sure you know the conditions necessary for a theorem to apply.
6. Before an exam take the practice exam under the same conditions as the exam is given, namely make sure you have no cheat sheets, books, solutions, calculators etc... Also pay attention to the time allowed and time yourself appropriately.
13. Look at homework as an exercise to build basic skills and look at tutorials as an opportunity to get practice on the next level of problems(worksheets) and an opportunity to practice in exam taking conditions (on your quizzes).
15. Try to see where calculus is applied in your other subjevcts, Physics, Economics, Chemistry,... Try to get past the differences in notation and see how the concepts are used. Seeing these connections means you will have less memorization to do in other subjects.
5. Keep in mind that if you want to learn soccer, you do not watch your coach paly soccer, you must practice to learn the skills involved. Similarly, you must try problems yourself to learn mathematics. The more you challenge yourself, the more you learn
6. Just as in learnng a sport, some activities are designed to build foundational skills and some are designed to fine tune your skills or to teach you to put together your basic skills to solve more complex problems. In this course, the basics are learned and practiced by doing homework, more complex challenges are given in the form of old exam questions and worksheets at tutorials. On exam day you meet a large complex challenge in the form of solving problems from a large chunk of material without props or references. You should do the groundwork in accquiring the basic skills way ahead of the exam and spend the week before your exam putting the basics together in a big picture and practicing more complex problems.
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