Advanced Calculus -  James J. Callahan

Advanced Calculus (eBook)

A Geometric View
eBook Download: PDF
2010 | 1. Auflage
526 Seiten
Springer New York (Verlag)
978-1-4419-7332-0 (ISBN)
Systemvoraussetzungen
67,82 inkl. MwSt
  • Download sofort lieferbar
  • Zahlungsarten anzeigen
With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus.  Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma.  The ideas behind most topics can be understood with just two or three variables.  The book incorporates modern computational tools to give visualization real power.  Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps.  The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books.  This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics.  Prerequisites are an introduction to linear algebra and multivariable calculus.  There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry.  The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.

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.
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.
Erscheint lt. Verlag 17.9.2010
Sprache englisch
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Technik
ISBN-10 1-4419-7332-X / 144197332X
ISBN-13 978-1-4419-7332-0 / 9781441973320
Haben Sie eine Frage zum Produkt?
PDFPDF (Wasserzeichen)
Größe: 9,8 MB

DRM: Digitales Wasserzeichen
Dieses eBook enthält ein digitales Wasser­zeichen und ist damit für Sie persona­lisiert. Bei einer missbräuch­lichen Weiter­gabe des eBooks an Dritte ist eine Rück­ver­folgung an die Quelle möglich.

Dateiformat: PDF (Portable Document Format)
Mit einem festen Seiten­layout eignet sich die PDF besonders für Fach­bücher mit Spalten, Tabellen und Abbild­ungen. Eine PDF kann auf fast allen Geräten ange­zeigt werden, ist aber für kleine Displays (Smart­phone, eReader) nur einge­schränkt geeignet.

Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen dafür einen PDF-Viewer - z.B. den Adobe Reader oder Adobe Digital Editions.
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen dafür einen PDF-Viewer - z.B. die kostenlose Adobe Digital Editions-App.

Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.

Mehr entdecken
aus dem Bereich