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A First Course in Calculus (Undergraduate Texts in Mathematics) 5th Edition

4.5 out of 5 stars 11 customer reviews
ISBN-13: 978-0387962016
ISBN-10: 0387962018
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Product Details

  • Series: Undergraduate Texts in Mathematics
  • Hardcover: 731 pages
  • Publisher: Springer; 5th edition (March 16, 1998)
  • Language: English
  • ISBN-10: 0387962018
  • ISBN-13: 978-0387962016
  • Product Dimensions: 6.1 x 1.6 x 9.2 inches
  • Shipping Weight: 2.4 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (11 customer reviews)
  • Amazon Best Sellers Rank: #897,955 in Books (See Top 100 in Books)

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By N. F. Taussig on July 31, 2008
Format: Hardcover
Serge Lang's text does an effective job of teaching you the skills you need to solve challenging calculus problems, while teaching you to think mathematically. The text is principally concerned with how to solve calculus problems. Key concepts are explained clearly. Methods of solution are effectively demonstrated through examples. The challenging exercises reinforce the concepts, while enabling you to develop the skills required to solve hard problems. Answers to the majority of exercises (not just the odd-numbered ones) are provided in a hundred page appendix, making this text suitable for self-study. In some sections, such as related rates and max-min problems, Lang provides many fully worked out solutions.

As effectively as Lang conveys the key concepts and teaches you how to solve problems, he does not neglect the subject's logical development. Topics are introduced only after their logical foundations have been laid. Results are derived. Theorems are proved when Lang feels that they will add to the reader's understanding. Through his exposition and his grouping of logically related exercises, Lang teaches the reader how a mathematician thinks about the subject.

The book is divided into five sections: review of basic material, differentiation and elementary functions, integration, Taylor's formula and series, and functions of several variables. The heart of the course is the middle three sections.

Most of the topics covered in the review of basic material should be familiar to most readers.
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Format: Hardcover
This book by the late Prof. Lang covers calculus in a clear and concise manner. I own more than a few
calculus books and this book is one of my favorites. The book looks like a math
book in that it is not a 1200 page glossy coloring book with multi-colored inserts on every
page. I think that the style of this book is a hugh improvement over most of the books on the market. I think a student who
buys this book along with a good calculus study guide would be very well set.
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Format: Hardcover
I had to take a refresher calculus course as a prerequisite to get into graduate school, but the assigned text (Edwards and Penney) was horrible. Like every other mass market calculus, it was filled with colorful diagrams and digressions on how to use calculators, but little in the way of explanation. Fortunately I found Lang's calculus in the university book store and it cured all of my problems. Unlike the bloated E&P, Lang's book is clear and concise. E&P covers more material to be sure, but for the essentials nothing beats Lang. After reading this book calculus became easy for me again. Which is as it should be, since calculus is a surprisingly simple subject if expalined well.
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Format: Hardcover Verified Purchase
I needed to bring my high school calculus up to speed for first year physics studies and found this to be the only book which covered the necessary ground. The material is presented in a thorough manner with the great majority of topics shown with proofs. The book is very well organized and there are abundant worked examples. Some problems are offered which deal with matters not covered in the text, but usually there is a worked example given among the answers. Lang deals with the material in a clear fashion so that the subject matter is usually not difficult to follow.On the negative side I can say that there is no human touch between the covers. His sole attempt at humor is an item following a list of problems in which he notes "relax". In the foreword he exhibits his firm belief that many freshmen arrive unprepared for college calculus, which may be true. But nowhere in the book is there a note of encouragement, so it cannot be described as reader friendly. Finally the index is pathetic--just three pages for a book of 624 pages, so that finding things can be frustrating.
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Format: Hardcover
The book is OK, but I wouldn't say it's great. There are lots of exercises that
ask you to do simple symbolic manipulation so you'll remember rules -- but there are
too few exercises that require the reader to actually think harder and be creative. The explanations are often shallow and not as stimulating as they could be, in my opinion.

Some examples of sections that I think are not well written are the one about implicit differentiation (the discussion is too short and not clear, and there are less exercises in this section than in others); the one about rate of change (some examples are boring, like "find the rate of change of the area of a circle given the rate of change of its diameter"; he does not make it clear that he's always derives with relation to time and that, for example, the radius and height of a cylinder should be understood as functions of time, so there's a feeling of sloppiness).

It's a good book,anyway. Now, it becomes a really great book when compared to the
colorful, flashy books available today.
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Format: Hardcover Verified Purchase
First, this text is not the most comprehensive and does lack rigor. Specifically the author avoids taking the examples beyond the most basic and there is no progression of building on examples to eventually illustrate the harder cases.

However, in the context of being a "first course" it fits that goal 100%. This book is why using older textbooks is actually a good idea. The organization is different than modern texts, which might prep for SAT's, but they are not always great for novice students.

The downside to older textbooks is that the format is usually different in how they approach various topics. The treatment of limits in this book is similiar to other older texts I have. Even Morris Kline's book seems to follow this pattern.

So a high school student would probably not be ready for the SAT's with this book, but they will at least learn Calculus in a very straightforward manner.

For self study or adult learners this book is better than any "dummies" book. ( not better than Kline's Calc book ) but better than stewart or larson for getting back in touch or learning Calculus for the first time.
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