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Understanding Calculus, by H. S. Bear
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Everything you need to know-basic essential concepts-about calculus
For anyone looking for a readable alternative to the usual unwieldy calculus text, here's a concise, no-nonsense approach to learning calculus. Following up on the highly popular first edition of Understanding Calculus, Professor H. S. Bear offers an expanded, improved edition that will serve the needs of every mathematics and engineering student, or provide an easy-to-use refresher text for engineers.
Understanding Calculus, Second Edition provides in a condensed format all the material covered in the standard two-year calculus course. In addition to the first edition's comprehensive treatment of one-variable calculus, it covers vectors, lines, and planes in space; partial derivatives; line integrals; Green's theorem; and much more. More importantly, it teaches the material in a unique, easy-to-read style that makes calculus fun to learn. By explaining calculus concepts through simple geometric and physical examples rather than formal proofs, Understanding Calculus, Second Edition, makes it easy for anyone to master the essentials of calculus.
If the dry "theorem-and-proof" approach just doesn't work, and the traditional twenty pound calculus textbook is just too much, this book is for you.
- Sales Rank: #1125218 in Books
- Published on: 2003-03-06
- Released on: 2003-02-20
- Ingredients: Example Ingredients
- Original language: English
- Number of items: 1
- Dimensions: 9.98" h x .59" w x 7.03" l, 1.18 pounds
- Binding: Paperback
- 320 pages
Review
"...expands coverage to vectors and calculus of several variables...plenty of worked out problems..." (American Mathematical Monthly, August/September 2003)
"...material included is well formulated and approachable...recommended." (Choice, Vol. 41, No. 1, September 2003)
From the Back Cover
Everything you need to know–basic essential concepts–about calculus
For anyone looking for a readable alternative to the usual unwieldy calculus text, here’s a concise, no-nonsense approach to learning calculus. Following up on the highly popular first edition of Understanding Calculus, Professor H. S. Bear offers an expanded, improved edition that will serve the needs of every mathematics and engineering student, or provide an easy-to-use refresher text for engineers.
Understanding Calculus, Second Edition provides in a condensed format all the material covered in the standard two-year calculus course. In addition to the first edition’s comprehensive treatment of one-variable calculus, it covers vectors, lines, and planes in space; partial derivatives; line integrals; Green’s theorem; and much more. More importantly, it teaches the material in a unique, easy-to-read style that makes calculus fun to learn. By explaining calculus concepts through simple geometric and physical examples rather than formal proofs, Understanding Calculus, Second Edition, makes it easy for anyone to master the essentials of calculus.
If the dry "theorem-and-proof" approach just doesn’t work, and the traditional twenty pound calculus textbook is just too much, this book is for you.
About the Author
H. S. BEAR, PhD, is a prolific author who has published several pre-calculus texts and an intermediate-level differential equations text, in addition to numerous research articles. His most recent works include two more advanced texts in analysis: A Primer of Lebesgue Integration, Second Edition and An Introduction to Mathematical Analysis. A dedicated educator, Dr. Bear has taught at six major western state universities before moving to Hawaii, where he has spent most of his career. Dr. Bear has served both as Department Chairman and Graduate Chairman at the University of Hawaii.
Most helpful customer reviews
6 of 6 people found the following review helpful.
Depends what you want ...
By Amazon Customer
Both previous reviewers are correct.
If you are a mathematician, this book is not for you. For a more rigorous, yet brief, alternative try "Short Calculus" by Serge Lang.
If, on the other hand, you are an applied scientist or engineer, this book does what it says on the tin, providing brief introductions to almost all calculus concepts you are likely to need for applied problem solving. Some previous exposure would be beneficial as the book is highly concise.
4 of 4 people found the following review helpful.
ideal first calculus text, especially for for non-math majors
By sp
I still remember my freshman year 25+ years ago as an undergraduate student and the 1300 page phone book that passed as a calculus text. Thinking back to this time, I recall how
much I hated the approach taken to teaching calculus to a large (200-300 people) diverse
class at a major university. Basically, neither the theory or the important ideas and insights were very well described by the mathematics professor or the textbook. At best, an engineering or physics student could learn the techniques of calculus in order to use them in further classes. Many math professors operate under the fallacy (in my opinion at least) that a first college level
calc class is a major failure
if it does not impart to all students the eps/delta scaffolding that the theory of the derivative and integral are based on. I would argue, that although this is a noble goal to achieve, in the end almost everyone in the
class winds up disappointed for various reasons. In my experience at least, most students resist the
rigor. ( For good reason as the ideas are very intricate and took some of the best minds after Newton/Leibniz to refine).
A first course in calculus should teach techniques and discuss ideas and concepts. Those students who need further analysis will be taught the rigor later. However, most people in a freshman calculus
class simply have no need for abstract analysis. Prof. Bear knows this full well and his book is his way of
addressing the problems just discussed. This book is short, well-written, and to the point. The
essentials of calculus are taught in the way one human being would teach another, not like the usual phone book size calculus book which tries to meet the needs of every student present and future.
This book is like a set of typed lecture notes for a real class. In any case, I would have
liked this book far better than the one I used 20+ years ago.
Why only 4 stars then? The discussion of limits needs to be a bit longer than the few sentences provided in the text.
Without going into eps/delta too far, the idea of limit should have been fleshed out a bit more.
After all, the limiting process is what distinguishes calculus from all math that comes before. However, in the real world, it is the techniques of calculus that should be
mastered first. Those who need the refinements will go seek them if and when the time is right.
2 of 2 people found the following review helpful.
a real missed opportunity to create a better calculus book
By A.Reader1
I have mixed feelings about this textbook.
Firstly, I'll agree with the author - we have far too many 1000 page calculus books on the market better suited to weightlifting than instruction. Lots of these ungainly textbooks try to please everyone by throwing everything and the kitchen sink into print. Seems no one tries to figure out which topics are core, which can be de-emphasized and which can be removed.
So, in response Prof. Bear has come up with an abbreviated work of only 272 pages designed to meet the needs of the vast majority of students taking first year university calculus. Unfortunately, he's over-corrected by making the book too short when he was probably intending to strike a better balance between theory, comprehensiveness and practical application. The current book is heavy on the practical aspects with little theory. He's also included some advanced material (differential equations, vector calculus, Green's theorem) better suited to year 2 of a typical undergraduate curriculum. He hardly delves into limits which is quite an accomplishment for a calculus book!
I do like that the end-of-chapter problem sets contain only about 20 - 35 questions. Students should be able to complete all of them and, if having done so, will feel the chapter material has been mastered. No need for endless number of problems. However, there are too many problems of the rote variety and more "word problems" should have been included.
I suppose this text could be used in a 1st year course but only if the instructor addresses the missing theory during class and those topics missing from the book. It'd be very good for community college or high school even.
For those of you who want a book that's comprehensive, covers theory and practice, is straight to the point and of ideal length (~600 pages) try "The Chemistry Maths Book" 2nd edition by Erich Steiner. It has most everything you need vis-à-vis calculus and related topics.
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