Advanced Calculus A Geometric View

ISBN-10: 1441973311
ISBN-13: 9781441973313
Edition: 2010
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Book details

Copyright year: 2010
Publisher: Springer
Publication date: 9/17/2010
Binding: Hardcover
Pages: 526
Size: 7.00" wide x 10.00" long x 1.25" tall
Weight: 2.904
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 &#8800; 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

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