Advanced Calculus: A Geometric View (Undergraduate Texts in Mathematics) - hardcover

EAN (ISBN-13): 9781441973313
ISBN (ISBN-10): 1441973311
Hardcover
Paperback
Publishing year: 2010
Publisher: Springer
526 Pages
Weight: 1,159 kg
Language: eng/Englisch

Book in our database since 2009-08-25T19:06:36-04:00 (New York)
Detail page last modified on 2022-06-22T05:17:21-04:00 (New York)
ISBN/EAN: 9781441973313

ISBN - alternate spelling:
1-4419-7331-1, 978-1-4419-7331-3

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Information from Publisher

Author: James J. Callahan
Title: Undergraduate Texts in Mathematics; Advanced Calculus - A Geometric View
Publisher: Springer; Springer US
526 Pages
Publishing year: 2010-09-17
New York; NY; US
Printed / Made in
Weight: 2,550 kg
Language: English
69,50 € (DE)
71,45 € (AT)
93,59 CHF (CH)
POD
XVI, 526 p.

BB; Book; Hardcover, Softcover / Mathematik/Analysis; Reelle Analysis, Real-Variablen; Verstehen; Algebra; Derivative; Green's theorem; Morse's lemma; Riemann and Darboux integrals; Stokes' theorem; calculus; change of variables formula; critical points; derivative as linear approximation; differential equation; implicit functions; inverse function theorem; parametrized surfaces; surface integrals; B; Real Functions; Analysis; Applications of Mathematics; Approximations and Expansions; Real Functions; Analysis; Applications of Mathematics; Approximations and Expansions; Mathematics and Statistics; Mathematische Analysis, allgemein; Angewandte Mathematik; Differentialrechnung und -gleichungen; EA; BC

1 Starting Points.-1.1 Substitution.- Exercises.- 1.2 Work and path integrals.- Exercises.- 1.3 Polar coordinates.- Exercises.- 2 Geometry of Linear Maps.- 2.1 Maps from R2 to R2.- Exercises.- 2.2 Maps from Rn to Rn.- Exercises.- 2.3 Maps from Rn to Rp, n 6= p.- Exercises.- 3 Approximations.- 3.1 Mean-value theorems.- Exercises.- 3.2 Taylor polynomials in one variable.- Exercises.- 3.3 Taylor polynomials in several variables.- Exercises.- 4 The Derivative.- 4.1 Differentiability.- Exercises.- 4.2 Maps of the plane.- Exercises.- 4.3 Parametrized surfaces.- Exercises.- 4.4 The chain rule.- Exercises.- 5 Inverses.- 5.1 Solving equations.- Exercises.- 5.2 Coordinate Changes.- Exercises.- 5.3 The Inverse Function Theorem.- Exercises.- 6 Implicit Functions.- 6.1 A single equation.- Exercises.- 6.2 A pair of equations.- Exercises.- 6.3 The general case.- Exercises.- 7 Critical Points.- 7.1 Functions of one variable.- Exercises.- 7.2 Functions of two variables.- Exercises.- 7.3 Morse’s lemma.- Exercises.- 8 Double Integrals.- 8.1 Example: gravitational attraction.- Exercises.- 8.2 Area and Jordan content.- Exercises.- 8.3 Riemann and Darboux integrals.- Exercises.- 9 Evaluating Double Integrals.- 9.1 Iterated integrals.- Exercises.- 9.2 Improper integrals.- Exercises.- 9.3 The change of variables formula.- 9.4 Orientation.- Exercises.- 9.5 Green’s Theorem.- Exercises.- 10 Surface Integrals.- 10.1 Measuring flux.- Exercises.- 10.2 Surface area and scalar integrals.- Exercises.- 10.3 Differential forms.- Exercises.- 11 Stokes’ Theorem.- 11.1 Divergence.- Exercises.- 11.2 Circulation and Vorticity.- Exercises.- 11.3 Stokes’ Theorem.- 11.4 Closed and Exact Forms.- Exercises
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.