Product Description

The pebbles used in ancient abacuses gave their name to the calculus, which today is a fundamental tool in business, economics, engineering and the sciences. This introductory book takes readers gently from single to multivariate calculus and simple differential and difference equations. Unusually the book offers a wide range of applications in business and economics, as well as more conventional scientific examples. Ideas from univariate calculus and linear algebra are covered as needed, often from a new perspective. They are reinforced in the two-dimensional case, which is studied in detail before generalisation to higher dimensions. Although there are no theorems or formal proofs, this is a serious book in which conceptual issues are explained carefully using numerous geometric devices and a wealth of worked examples, diagrams and exercises. Mathematica has been used to generate many beautiful and accurate, full-colour illustrations to help students visualise complex mathematical objects. This adds to the accessibility of the text, which will appeal to a wide audience among students of mathematics, economics and science.

Product Details

• Amazon Sales Rank: #291935 in Books
• Published on: 2002-02-07
• Original language: English
• Number of items: 1
• Binding: Paperback
• 500 pages

Review
‘… well illustrated and has a good supply of examples and exercises … an excellent textbook for courses in intermediate calculus for students of mathematics as well as economics.’ Zentralblatt für Mathematik

‘The book not only broadens one's mathematical scope and improves one's mathematical skill but, even more usefully, it shows the reader how powerful are the tools that mathematics offers, and that mathematics allows us to participate in processes where our presence is impossible: through mathematics we can enter forbidden worlds, through mathematics we can see the future. Although the book contains no formal definitions, theorems or proofs, it is a genuine mathematical textbook showing how and why the explained methods and concepts work. One hardly can imagine a better textbook of this type.‘ EMS

‘… a welcome addition to the ever increasing library of texts introducing the calculus of several real variables. The book is carefully thought out and well written with its target audience always in mind.‘ The Mathematical Gazette

Customer Reviews

An outstanding book
This book would also be of considerable value to physicists and engineers, although the primary audience is probably economists. The aproach is a thoroughly modern one of using a linear algebra approach to calculus.

The book makes no pretense about avoiding the formal definition-theorem-proof approach appropriate to a mathematician. It is not intended to be a rigorous approach. Instead, it focuses on geometric intuition and the "whys" as well as the "hows." The many excellent multi-colo(u)r diagrams are extremely helpful in explaining concepts. Although the book says that prerequisites are basic familiarity with single-variable calculus and linear algebra, the review sections on those topics are thorough enough to learn from, as long as the reader is not completely unfamiliar, by working through the carefully constructed exercises. In fact, the first chapter is, in of itself, an excellent primer on linear algebra.

My hope, for the next edition, is that the authors, having beautifully developed the vector calculus of Grad, might extend the development to Div and Curl (along the intuitive lines of Schey - Div, Grad, Curl and All That) to make the book even more appropriate to physicists/engineers.

If you want a crystal-clear exposition of multi-variable calculus, while learning linear algebra at the same time, this is THE book (and there is nothing else like it that I have seen out there). The book is wonderfully laid out, attractive to work through, and the examples and problem sets are first rate. I hesitate to say it, but I believe you will actually really enjoy the topic, whatever your previous misgivings about calculus may have been. If that is true, you will learn a tremendous amount from this book.

Bravo, the authors!

Calculus
This book is quite helpful when it comes to functions of one variable and several variables. I found the chapter on linear differential and difference equations a bit hard to grasp, finding other texts more appropriate for the job. Generally the book seems ok