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Title: Calculus: Graphical, Numerical, and Algebraic
ISBN: 0201324458
Author:
Franklin Demana
Bert K. Waits
Daniel Kennedy
Publicate Date: 1999-01
Publish: 1999-01
List Price: $107.20
Average Customer Rating: 3.0
Format: Hardcover
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Amazon Lowest New Price: $30.00
Amazon Lowest Used Price: $6.00
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| Customer Review: |
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1: Hated it as a student, but it's a good book
I used this textbook when I took AP Calculus. I recall not liking it very much -- my mathematics preparation was poor, and I struggled to understand the precise statements of definitions and theorems. It didn't help that at the time I was only concerned with what would be on the AP exam, naively believing the Collegeboard propaganda that an AP exam represented the equivalent of a college-level course.
Revisiting this book years later, having taken college math classes where it's sink or swim -- and you sink if you don't read the textbook -- I appreciate this book a lot more. It is fairly rigorous but never too much so, and practice problems abound. My only regret is not reading this book while I was still in high school. Like many calculus students, I went into the AP exam very skilled at taking AP Calculus exams, but with very little knowledge of calculus; I could compute integrals or solve related rates problems without too much trouble, but if anyone were to push me on my foundations, I would fall flat on my face. It didn't help that my teacher knew very little calculus himself and let theory fall by the wayside in favor of computational examples. If there are any current AP Calculus students reading this, if you don't see why the Mean Value Theorem is the cornerstone of calculus, then you haven't really learned the subject!
I was not alone in finding this book difficult to read as a high school student -- my classmates then and my students now have expressed similar opinions. However, this is not a fault of the text, but a reflection of the declining standards of math education -- throughout high school, my math teachers spoon-fed the formulas I needed to know, and I was never forced to grapple with mathematics exposition on my own. This text is certainly much more informal and accessible than my multivariable calc text freshman year of college. If there are any high school math teachers reading this, I hope that you do not make the same mistake that my teachers made and that you encourage your students to read textbooks like this. It is a skill that they will need in college!
As much as I love this book now for its clarity, I realize that it is easy to find something clear when you already understand it. I can sympathize with the high schooler who is seeing power series for the first time and trying to understand the terse explanations in this text. Some of the concepts are crudely explained, and the book gets too carried away with the "graphing approach" nonsense. The ridiculous number of "try graphing this to see..." investigations come at the cost of additional examples and clarifications for students who actually want to use the text as a reference. I also don't understand why certain homework problems are labeled "Work in groups of two or three" when they are no different from the other problems. I guess this superfluous instruction could easily be ignored, but it reeks of a tacky marketing gimmick ("interactive learning") to me.
The sequencing of topics in this text vacillates between excellent and awful. The treatment of the material in Chapters 1-5 is basically flawless, but it falls apart beginning in Chapter 6. The chapter is titled "Differential Equations and Mathematical Modeling," but it includes such sections as "Integration by Substitution" and "Integration by Parts," which don't seem particularly relevant to differential equations -- or mathematical modeling, for that matter. I would have preferred that these techniques of integration be grouped with others, such as partial fractions and trig substitution, which somehow ended up in Chapter 8. Speaking of Chapter 8, what exactly is supposed to be the unifying element of a chapter entitled "L'Hopital's Rule, Improper Integrals, and Partial Fractions"? It almost seems as if the authors finished realized at the last minute that they forgot to cover these three topics and threw them into one chapter.
I am nitpicking, and really, I do quite like this book. Unlike other recent calculus textbooks, it doesn't try to dumb down the math (I especially like the appendix on epsilon-delta!), and the exposition is quite clear. Nonetheless, this book would be much improved if it ditched the gimmicks, stuck to the math, and presented the material in a more methodical fashion.
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2: The Reason People Think Calculus Is "Hard"
Calculus is far from difficult. It's different, but not difficult. In an attempt to be terse, this book loses all of the things essential to getting a student to understand calculus: good examples, explanations, and a logical progression of difficulty. There are many ways to explain a mathematical concept, but you're lucky if you get a single coherent one out of this book. It needs to be supplemented so much -- to the point of it being just plain useless. I'm all for lighter, briefer textbooks, but not when brevity impedes on quality. It's sufficient for getting a student to pass the AP exam, in some cases, but that's not the goal. The goal is for students to understand calculus and, more importantly, better understand mathematics as a whole.
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3: The bane of my existence
I am currently a senior in high school working my way through this book for my AB Calculus class. All I can say is that this is the crappiest textbook I've ever come across in my life, and I mean it. The concepts are presented poorly with very few examples. The examples that they do give are hard to follow and often times will not help you with the problems you will soon encounter. As life would have it, my math teacher is of no help either, which only makes things worse. If you know you will have this textbook for Calc beforehand, heed my warnings and learn from a different book if you can. Save yourself from this nightmare that will haunt you for the rest of your life.
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4: A Great Book For Its Purpose
I am currently a senior in High School, and I am in Advanced Placement Calculus. The textbook we use is the next edition of this text, but the textbooks are pratically identical, so i decided to comment here. This text is designed to be an introductary text. Introductary texts teach you concepts that you should be able to understand how to use. A lot of these concepts are too advanced to be explained in an introductary course, so they are omitted from the text. Learning math is just like learning anything else. You must first learn how to do it, and then you must learn why you do it. This text tells you what to do with minimal explations because long explainations make readers lose attention and the why would be gone anyway. One other thing that this book does is it gives previews into the next section. Obviously, concepts build upon one another, so some of the problems in the exercises are designed to try and make you think outside the box and get a glimpse into the next section.
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5: Frustration Maxima
This text has simple examples that are only moderately easy to follow. The problems, on the other hand, are extremely difficult. There is no bridge between the two. The index is not particularly good. The explanations are obscure. The text spends too much time on theory that I suppose is interesting to mathematicians, but just gets in the way of learning about derivatives and integrals and their uses. I truly detest this book and find it a misery to deal with. My child's teacher was sick for the first half of the year, so I was thrust into the breach. I graduated from college magna cum laude with a Phi Beta Kappa key, I took Calculus and made an A (many years ago), I am a CPA with an MBA. My difficulties were not because I am dumb and not because I wasn't trying.
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