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Calculus: An introduction to applied mathematics Hardcover – June 1, 1997


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Product Details

  • Hardcover: 784 pages
  • Publisher: Breukelen Press; 1 edition (June 1, 1997)
  • Language: English
  • ISBN-10: 0962699810
  • ISBN-13: 978-0962699818
  • Product Dimensions: 9.1 x 6.3 x 2 inches
  • Shipping Weight: 2.6 pounds
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #4,095,176 in Books (See Top 100 in Books)

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10 of 10 people found the following review helpful By jeff on December 10, 2000
Format: Hardcover
This book is very clear, with many neat, simple and effective igures. It has extremely interesting and challenging examples and topics from applied mathematics (particularly fluid dynamics) which are very well explained given their complexity. In addition this book is a bargin at only 55 dollars, and has good problems with solutions in the back. recommened to anyone learning calculus on their own or looking for a nice, compact, cheap reference book on calculus (covers through multi-dimensional caluculs with excellent emphasis on vector calculus)
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1 of 1 people found the following review helpful By Mark Kluge on April 28, 2013
Format: Hardcover
This wonderful book is everything that "reform calculus" should have been. Reform calculus was a movement in the 1980s to make calculus instruction more accessible to science and engineering students. It was thought that excessive and misplaced mathematical rigor was getting in the way of calculus instruction. The result was often dumbed down calculus courses. Greenspan and Benny also deemphasize mathematical rigor, but its sheer breadth of topics covered and diversity of problems ensure an intellectually exhilarating and challenging calculus course.

How well I remember first reading this book while in high school. On page 79, Example 3, the student is asked to find the roots of the equation x^2 + a*x - 4 = 0 as a function of the parameter a. Obviously one could just use the quadratic formula, but suppose that one did not know the quadratic formula. What would one do then? Greenspan and Benn use this example to introduce the student to the idea of perturbation series. For a small the roots are obviously going to be close to +-2. Greenspan and Benny demonstrate how to systematically expand the unknown x in a formal power series x = x0 + x1*a + x2*a^2..., and how to find the coefficients x0, x1, x2... I was hooked right there! What other calculus text book would introduce perturbation series so early? The mathematical treatment is rough and dirty, but this book emphasizes and demonstrates the sheer power and breadth of applications of calculus like no other.

All the standard topics are covered, including limits and continuity, but Greenspan and Benny don't emphasize mathematical rigor. A student wishing to explore the detailed mathematical foundations of calculus might wish to look elsewhere. What this book has like no other is breadth, brevity and beauth of coverage.
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