Advanced Calculus A Geometric View

Name: Advanced Calculus A Geometric View
Availability: InStock
ISBN: 9781441973313

ISBN-10: 1441973311

ISBN-13: 9781441973313

Edition: 2010

Authors: James J. Callahan

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Book details

List price: $84.95
Copyright year: 2010
Publisher: Springer New York
Publication date: 9/17/2010
Binding: Hardcover
Pages: 526
Size: 7.00" wide x 10.00" long x 1.25" tall
Weight: 2.750
Language: English




Starting Points



Substitution



Work and path integrals



Polar coordinates


Exercises



Geometry of Linear Maps



Maps from R<sup>2</sup> to R<sup>2</sup>



Maps from R<sup>n</sup> to R<sup>n</sup>



Maps from R<sup>n</sup> to R<sup>p</sup>, n ≠ p


Exercises



Approximations



Mean-value theorems



Taylor polynomials in one variable



Taylor polynomials in several variables


Exercises



The Derivative



Differentiability



Maps of the plane



Parametrized surfaces



The chain rule


Exercises



Inverses



Solving equations



Coordinate changes



The inverse function theorem


Exercises



Implicit Functions



A single equation



A pair of equations



The general case


Exercises



Critical Points



Functions of one variable



Functions of two variables



Morse's lemma


Exercises



Double Integrals



Example: gravitational attraction



Area and Jordan content



Riemann and Darbou integrals


Exercises



Evaluating Double Integrals



Interated integrals



Improper integrals



The change of variables formula



Orientation



Green's theorem


Exercises



Surface Integrals



Measuring flux



Surface area and scalar integrals



Differential forms


Exercises



Stokes' Theorem



Divergence



Circulation and vorticity



Stokes' theorem



Closed and exact forms


Exercises


References


Index