Callahan | Advanced Calculus | Buch | 978-1-4939-4070-7 | sack.de

Buch, Englisch, 526 Seiten, Previously published in hardcover, Format (B × H): 178 mm x 254 mm, Gewicht: 1011 g

Reihe: Undergraduate Texts in Mathematics

Callahan

Advanced Calculus

A Geometric View
Softcover Nachdruck of the original 1. Auflage 2010
ISBN: 978-1-4939-4070-7
Verlag: Springer

A Geometric View

Buch, Englisch, 526 Seiten, Previously published in hardcover, Format (B × H): 178 mm x 254 mm, Gewicht: 1011 g

Reihe: Undergraduate Texts in Mathematics

ISBN: 978-1-4939-4070-7
Verlag: Springer


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.

Callahan Advanced Calculus jetzt bestellen!

Zielgruppe


Lower undergraduate


Autoren/Hrsg.


Weitere Infos & Material


Starting Points.- Geometry of Linear Maps.- Approximations.- The Derivative.- Inverses.- Implicit Functions.- Critical Points.- Double Integrals.- Evaluating Double Integrals.- Surface Integrals.- Stokes’ Theorem.


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.



Ihre Fragen, Wünsche oder Anmerkungen
Vorname*
Nachname*
Ihre E-Mail-Adresse*
Kundennr.
Ihre Nachricht*
Lediglich mit * gekennzeichnete Felder sind Pflichtfelder.
Wenn Sie die im Kontaktformular eingegebenen Daten durch Klick auf den nachfolgenden Button übersenden, erklären Sie sich damit einverstanden, dass wir Ihr Angaben für die Beantwortung Ihrer Anfrage verwenden. Selbstverständlich werden Ihre Daten vertraulich behandelt und nicht an Dritte weitergegeben. Sie können der Verwendung Ihrer Daten jederzeit widersprechen. Das Datenhandling bei Sack Fachmedien erklären wir Ihnen in unserer Datenschutzerklärung.