Home Newsletter
News Books
Welcome to FreeScience.info Language/Lingua

Books 3054
· Book News
· Most clicked
· Least clicked

Search for a Book
HELP US TO HELP YOU
Add a new Book

Calculus Unlimited

book
Language:
Author: Marsden, Jerrold and Weinstein, Alan
Url: http://caltechbook.library.caltech.edu/197/
Format: Pdf
Year: 1981
Category: Calculus
Pages: 200
Clicks: 3278

Description
This book is intended to supplement our text, Calculus (Benjamin/Cummings, 1980), or virtually any other calculus text (see page vii, How To Use This Book With Your Calculus Text). As the title Calculus Unlimited implies, this text presents an alternative treatment of calculus using the method of exhaustion for the derivative and integral in place of limits. With the aid of this method, a definition of the derivative may be introduced in the first lecture of a calculus course for students who are familiar with functions and graphs. Approach: Assuming an intuitive understanding of real numbers, we begin in Chapter 1 with the definition of the derivative. The axioms for real numbers are presented only when needed, in the discussion of continuity. Apart from this, the development is rigorous and contains complete proofs. As you will note, this text has a more geometric flavor than the usual analytic treatment of calculus. For example, our definition of completeness is in terms of convexity rather than least upper bounds, and Dedekind cuts are replaced by the notion of a transition point. Who Should Use This Book: This book is for calculus instructors and students interested in trying an alternative to limits. The prerequisites are a knowledge of functions, graphs, high school algebra and trigonometry. How To Use This Book: Because the "learning-by-doing" technique introduced in Calculus has proved to be successful, we have adapted the same format for this book. The solutions to "Solved Exercises" are provided at the back of the book; however readers are encouraged to try solving each example before looking up the solution. The Origin Of The Definition of The Derivative: Several years ago while reading Geometry and the Imagination, by Hilbert and Cohn-Vossen (Chelsea, 1952, p. 176), we noticed a definition of the circle of curvature for a plane curve C. No calculus, as such, was used in this definition. This suggested that the same concept could be used to define the tangent line and thus serve as a limit-free foundation for the differential calculus. We introduced this new definition of the derivative into our class notes and developed it in our calculus classes for several years. As far as we know, the definition has not appeared elsewhere. If our presumption of originality is ill-founded, we welcome your comments. Jerrold Marsden Alan Weinstein Berkeley, CA

Similar Books
Calculus Textbook
Multivariable Calculus
The Calculus Bible
Calculus Without Limits
Elementary Calculus: An Approach Using Infinitesimals
The Calculus of Functions of Several Variables
Multivariable Calculus
Advanced Calculus
Calculus Study Guide Components
Calculus Instructor's Manual Components
First Year Calculus
Differential and Integral Calculus: Volume 1
Differential and Integral Calculus
Vector Calculus
Whitman Calculus
JUST THE MATHS
Calculus: A modern, rigorous approach
ORDERS OF INFINITY
Calculus
Differential Calculus
Combinatorics and algebra of tensor calculus

Home |  Authors | About | Contact Us |  Email 
 Copyright © 2002-2013 FreeScience.info. 

Best viewed with Mozilla 1.X 1024x768
free scientific books