Striking a balance between concepts, modeling, and skills, this highly acclaimed book arms readers with an accessible introduction to calculus. It builds on the strengths from previous editions, presenting key concepts graphically, numerically, symbolically, and verbally. Guided by this innovative Rule of Four approach, the fourth edition examines new topics while providing readers with a strong conceptual understanding of the material.
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23 of 23 people found the following review helpful:
1.0 out of 5 stars
the cover looks nice,
By Dr. Chuck (California) - See all my reviews
This review is from: Calculus: Single and Multivariable (Hardcover)
I have a Ph.D. in math and teach at a college in California. I compared the Hughes-Hallett book with 7 other calculus books: Anton, Edwards, Larson, Rogawski, Smith, Stewart, Thomas. Here are some concerns with the Hughes-Hallett book.
This book is missing the following topics: reciprocal trigonometric functions (sec x, csc x, cot x), squeeze theorem, logarithmic differentiation, sketching graphs by hand by using derivatives, telescoping series, curvature, tangential and normal components of acceleration, line and surface integrals over scalar fields. All the other 7 books include these topics. Six series tests are crammed into section 9.4. None of the other 7 books cram all six of these series tests into one section. The Root Test for series is embedded into two homework problems. All of the other 7 books include the Root Test in a box within a section. Planes (12.4) are discussed before talking about vectors (chapter 13). All the other 7 books discuss vectors first and then use vectors to develop planes. Center of mass multiple integral formulas are embedded into the homework problems. All the other 7 books explain center of mass multiple integral formulas within a section. The preface reads, "Students are expected to use their own judgment to determine where technology is useful." All the other 7 books make it clear when the students should use technology. The preface reads, "There are very few examples in the text that are exactly like the homework problems. This means that you can't just look at a homework problem and search for a similar-looking `worked out' example." Many students learn calculus by seeing `worked out' examples. Instructors: If you are considering adopting this book, then you've been warned. Students: If you have to use this book, then go to class, do your homework, and good luck. Hope this information helps. Dr. Chuck
21 of 23 people found the following review helpful:
2.0 out of 5 stars
Falls short where it counts,
By Superannuated student (N. Calif.) - See all my reviews
This review is from: Calculus: Single and Multivariable (Hardcover)
(Commentary below refers to soft cover Third Edition.)
For those of us who learn by example and who need more active guidance through difficult material, this book falls short. It appears to be a deliberate design strategy of this book, to under-explain then over-exercise. This is tolerable until one gets to integration, where the sink-or-swim approach will result in many unnecessary drownings. Stewart seems at least a little better in this regard, and I note that it is replacing Hughes-Hallett in my school. One could hope some day for a text written by someone who had enough trouble learning the subject, to be able to remember the value of a patient explanation. No, 8 pages (including the exercises) are NOT sufficient to explain algebraic identities and trigonometric substitution in integration, except to a bright student with a fresh memory of trigonometry. The physical weight of this book is burdensome, and the price is symptomatic of the shameless shakedown racket that American textbook publishing has become. Some Web research reveals that a typical price for a German university mathematics text is under $50 equivalent.
20 of 22 people found the following review helpful:
3.0 out of 5 stars
I would not adopt it for my courses in calculus,
By Charles Ashbacher (Marion, Iowa United States) - See all my reviews (TOP 500 REVIEWER) (VINE VOICE) (HALL OF FAME REVIEWER)
This review is from: Calculus: Single and Multivariable (Hardcover)
I teach mathematics and computer science at a small college, so I examined this book for possible adoption as a text in our three class sequence in calculus. Since it does cover calculus all the way through flux integrals and the calculus of vector fields, there is certainly enough material for the sequence. One characteristic that I approved of was the lack of "using technology" segments.
In this area, I will be the first to admit that I am of the old school, even though I have taught a course in programming with Maple and am a heavy user of Mathematica. The reason why I disapprove of using these programs in calculus is that the students have enough on their minds without having to learn how to program a symbolic mathematics package. Learning calculus is very hard, all mathematics, especially calculus, is not a spectator sport. Some people liken it to a contact sport, as it can be very exhausting to learn it. Forcing the students to simultaneously learn programming is in my opinion too much to ask. There are plenty of exercises and solutions to the odd-numbered ones are included. However, I will not be adopting this book or recommending that it be adopted. I do not think the depth of the explanations is adequate. For example, on page 50 there is the epsilon-delta definition of a limit. After that, there is only one example (limit of 2x as x goes to 3) of how this definition is used to determine a limit. On the next page there is a theorem listing many of the properties of limits but no explanations as to why they are true. Proofs are largely nonexistent, the pedagogical style is to say, "here is something that is true" and then go immediately to an example of how it is used. I will readily concede that if that is your style of teaching calculus, then this book will work for you. However, if you want to occasionally give a true proof-style explanation as to why a property holds, then you are on your own.
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Inside This Book
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First Sentence:
In mathematics, a function is used to represent the dependence of one quantity upon another. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
central vector field, increasing function theorem, possible contour diagram, original integral diverges, tangent line approximation, curl test, find parametric equations, circulation density, continuous growth rate, nonzero circulation, local and global extrema, parameter rectangle, limit comparison test, robin population, local linearity, oriented counterclockwise, slope field, curl field, solid whose base, flux integral, nonzero terns, mann sum, use your solution, chirp rate, parameterized surface Key Phrases - Capitalized Phrases (CAPs): (learn more)
Divergence Theorem, New York, Exercises In Exercises, Ready Reference, Challenge Problems, Exercises For Exercises, Solution Let, Racetrack Principle, Solution Using, Hong Kong, Exercises Find, Constant Function Theorem, Solution First, Intermediate Value Theorem, Solution Figure, Solution Suppose, Coulomb's Law, Kepler's Second Law, Problems For Problems, Reading Island, United States, Civil War, Examples Find, Great Lakes, Problems In Problems New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In mathematics, a function is used to represent the dependence of one quantity upon another. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
central vector field, increasing function theorem, possible contour diagram, original integral diverges, tangent line approximation, curl test, find parametric equations, circulation density, continuous growth rate, nonzero circulation, local and global extrema, parameter rectangle, limit comparison test, robin population, local linearity, oriented counterclockwise, slope field, curl field, solid whose base, flux integral, nonzero terns, mann sum, use your solution, chirp rate, parameterized surface Key Phrases - Capitalized Phrases (CAPs): (learn more)
Divergence Theorem, New York, Exercises In Exercises, Ready Reference, Challenge Problems, Exercises For Exercises, Solution Let, Racetrack Principle, Solution Using, Hong Kong, Exercises Find, Constant Function Theorem, Solution First, Intermediate Value Theorem, Solution Figure, Solution Suppose, Coulomb's Law, Kepler's Second Law, Problems For Problems, Reading Island, United States, Civil War, Examples Find, Great Lakes, Problems In Problems New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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