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A First Course in Calculus (Undergraduate Texts in Mathematics) [Hardcover]

by Serge Lang
4.5 out of 5 stars  See all reviews (8 customer reviews)

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Book Description

March 1, 1998 0387962018 978-0387962016 5th
This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. Divided into five parts, each section of A FIRST COURSE IN CALCULUS contains examples and applications relating to the topic covered. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions.

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A First Course in Calculus (Undergraduate Texts in Mathematics) + Calculus of Several Variables (Undergraduate Texts in Mathematics) + Introduction to Linear Algebra (Undergraduate Texts in Mathematics) 2nd edition
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Product Details

  • Series: Undergraduate Texts in Mathematics
  • Hardcover: 731 pages
  • Publisher: Springer; 5th edition (March 1, 1998)
  • Language: English
  • ISBN-10: 0387962018
  • ISBN-13: 978-0387962016
  • Product Dimensions: 9.4 x 6.3 x 1.8 inches
  • Shipping Weight: 2.4 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (8 customer reviews)
  • Amazon Best Sellers Rank: #512,618 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
23 of 24 people found the following review helpful
4.0 out of 5 stars Effectively conveys key concepts and skills. July 31, 2008
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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13 of 13 people found the following review helpful
5.0 out of 5 stars shines without all the bling and flash June 24, 2007
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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27 of 31 people found the following review helpful
4.0 out of 5 stars Calculus for beginning college students August 28, 2002
By A Customer
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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12 of 12 people found the following review helpful
5.0 out of 5 stars Promotes real understanding of calculus March 26, 2008
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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