Advanced Calculus : A Geometric View

James J. Callahan

ISBN 10: 1493940708 / ISBN 13: 9781493940707

Published by Springer, Springer, 2016

About this Item

Druck auf Anfrage Neuware - Printed after ordering - A half-century ago, advanced calculus was a well-de ned subject at the core of the undergraduate mathematics curriulum. The classic texts of Taylor [19], Buck [1], Widder [21], and Kaplan [9], for example, show some of the ways it was approached. Over time, certain aspects of the course came to be seen as more signi cant-those seen as giving a rigorous foundation to calculus-and they - came the basis for a new course, an introduction to real analysis, that eventually supplanted advanced calculus in the core. Advanced calculus did not, in the process, become less important, but its role in the curriculum changed. In fact, a bifurcation occurred. In one direction we got c- culus on n-manifolds, a course beyond the practical reach of many undergraduates; in the other, we got calculus in two and three dimensions but still with the theorems of Stokes and Gauss as the goal. The latter course is intended for everyone who has had a year-long introduction to calculus; it often has a name like Calculus III. In my experience, though, it does not manage to accomplish what the old advancedcalculus course did. Multivariable calculusnaturallysplits intothreeparts:(1)severalfunctionsofonevariable,(2)one function of several variables, and (3) several functions of several variables. The rst two are well-developed in Calculus III, but the third is really too large and varied to be treated satisfactorily in the time remaining at the end of a semester. To put it another way: Green's theorem ts comfortably; Stokes' and Gauss' do not.

Seller Inventory # 9781493940707

Bibliographic Details

• Title: Advanced Calculus : A Geometric View
• Publisher: Springer, Springer
• Publication Date: 2016
• Language: English
• ISBN 10: 1493940708
• ISBN 13: 9781493940707
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 254W x 178H x 30D millimeters 254 millimeters width by 178 millimeters height by 30 millimeters depth
• Weight: 1011 grams

About this title

Synopsis

A half-century ago, advanced calculus was a well-de?ned subject at the core of the undergraduate mathematics curriulum. The classic texts of Taylor [19], Buck [1], Widder [21], and Kaplan [9], for example, show some of the ways it was approached. Over time, certain aspects of the course came to be seen as more signi?cant―those seen as giving a rigorous foundation to calculus―and they - came the basis for a new course, an introduction to real analysis, that eventually supplanted advanced calculus in the core. Advanced calculus did not, in the process, become less important, but its role in the curriculum changed. In fact, a bifurcation occurred. In one direction we got c- culus on n-manifolds, a course beyond the practical reach of many undergraduates; in the other, we got calculus in two and three dimensions but still with the theorems of Stokes and Gauss as the goal. The latter course is intended for everyone who has had a year-long introduction to calculus; it often has a name like Calculus III. In my experience, though, it does not manage to accomplish what the old advancedcalculus course did. Multivariable calculusnaturallysplits intothreeparts:(1)severalfunctionsofonevariable,(2)one function of several variables, and (3) several functions of several variables. The ?rst two are well-developed in Calculus III, but the third is really too large and varied to be treated satisfactorily in the time remaining at the end of a semester. To put it another way: Green’s theorem ?ts comfortably; Stokes’ and Gauss’ do not.

About the Author

James J. Callahan is currently a professor of mathematics at Smith College. His previous Springer book is entitled The Geometry of Spacetime: An Introduction to Special and General Relativity. He was director of the NSF-funded Five College Calculus Project and a coauthor of Calculus in Context.