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This is a course text for introductory to advanced calculus. Topics include limits, differentiation, integration, series, vectors, partial differentiation, multiple integrals, and vector calculus. Material is presented with example and exercises are included.
- Sales Rank: #4054648 in Books
- Published on: 1986-02
- Number of items: 1
- Binding: Hardcover
Most helpful customer reviews
5 of 5 people found the following review helpful.
What Reform Calculus should have been
By Mark Kluge
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. What other introductory calculus text covers perturbation series, Lagrange Interpolation polynomials, operator methods in series, asymptotic series? It is said that Newton finally published his ideas on calculus after Edmond Halley asked him for his solution of the Kepler problem (motion of a planet under an inverse square central force). Yet few introductory calculus books dare to tackle that classic problem. Greenspan and Benny do it in this book! Numerical and computational issues are emphasized throughout the book. In this reviewer's opinion it does so than most contemporary calculus text books even though it was first published during the 1970s prior to the widespread availability of personal computers. The exercises contain a fair number of the usual plug-and-chug confidence-builders necessary in any text, but there are also numerous real applications (many from fluid mechanics) liberally scattered throughout the examples and exercises.
This book is densely written in the sense that there is little verbal baggage, and the text is choc full of practical advice for the budding applied mathematician. The pace is lively and quick, and the authors presume much of the student. If you are not highly motivated, and maybe just a little bit bright, then this book is not for you. This book was wonderful for my self-study more than thirty years ago. I'm not sure how well it would fare as the basis for a lecture class in calculus. In emphasizing applications (in the sense of applied mathematics, not in the sense of being dumbed down to the level of the average calculus student) the book does skimp on mathematical rigor. Many standard proofs are not given, and those that are given tend often to be sketchy and incomplete. The mathematically-minded reader might wish to supplement this with another text, such as that by Thomas Apostol. But for sheer breadth of coverage, to experience the ecstasy of seeing for the first time (or the umpteenth time!) the sheer power of what mathematics can do, this book has few peers. Unlike reform calculus, which sought to make calculus accessible to mediocre students, this text, by deemphasizing unnecessary rigor, and concentrating on both breadth and depth of applications, manages to "dumb up" calculus instruction for those who can handle it and want to grasp it.
12 of 12 people found the following review helpful.
Excellent, Challenging introduction to Applied math
By jeff
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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