Advanced Calculus

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. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. 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.

Offers important geometric approach to advanced calculus Integrates text fully with 250+ illustrations Treats classical advanced calculus topics Uses 2D and 3D graphics to study maps Magnifies images to carry out local analysis Gives visual insight into the derivative Gives geometric interpretation of implicit function theorems Analyzes physical meaning of divergence and curl Presents Morse's lemma and Poincaré lemma Includes supplementary material: sn.pub/extras Request lecturer material: sn.pub/lecturer-material

Autorentext
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.

Zusammenfassung
Over time, certain aspects of the course came to be seen as more signi?cantthose seen as giving a rigorous foundation to calculusand they - came the basis for a new course, an introduction to real analysis, that eventually supplanted advanced calculus in the core.

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