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Advanced Calculus: A Geometric View James J. Callahan Author
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Advanced Calculus: A Geometric View James J. Callahan Author - nuovo livro

ISBN: 9781441973313

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—t… mais…

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Advanced Calculus
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Advanced Calculus - nuovo livro

ISBN: 9781441973313

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… mais…

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Advanced Calculus: A Geometric View (Undergraduate Texts in Mathematics) A Geometric View - Callahan, James J.
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Callahan, James J.:
Advanced Calculus: A Geometric View (Undergraduate Texts in Mathematics) A Geometric View - encadernada, livro de bolso

2009

ISBN: 1441973311

Auflage: 2010 hardcover 542 Seiten Gebundene Ausgabe 9781441973313 critical points, surface integrals, Stokes' theorem, parametrized surfaces, inverse function theorem, change of variabl… mais…

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Advanced Calculus: A Geometric View (Undergraduate Texts in Mathematics) [Hardcover] Callahan, James J. - Callahan, James J.
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Callahan, James J.:
Advanced Calculus: A Geometric View (Undergraduate Texts in Mathematics) [Hardcover] Callahan, James J. - encadernada, livro de bolso

2010, ISBN: 1441973311

[EAN: 9781441973313], [SC: 3.0], [PU: Springer], Unread, some shelfwear, Books

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Advanced Calculus - James J. Callahan
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James J. Callahan:
Advanced Calculus - encadernada, livro de bolso

2010, ISBN: 9781441973313

A Geometric View, Buch, Hardcover, [PU: Springer-Verlag New York Inc.], Springer-Verlag New York Inc., 2010

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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. 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.

Dados detalhados do livro - Advanced Calculus


EAN (ISBN-13): 9781441973313
ISBN (ISBN-10): 1441973311
Livro de capa dura
Livro de bolso
Ano de publicação: 2010
Editor/Editora: Springer-Verlag New York Inc.
526 Páginas
Peso: 1,159 kg
Língua: eng/Englisch

Livro na base de dados desde 2009-08-25T20:06:36-03:00 (Sao Paulo)
Página de detalhes modificada pela última vez em 2024-03-03T11:58:20-03:00 (Sao Paulo)
Número ISBN/EAN: 9781441973313

Número ISBN - Ortografia alternativa:
1-4419-7331-1, 978-1-4419-7331-3
Ortografia alternativa e termos de pesquisa relacionados:
Autor do livro: james, callahan
Título do livro: undergraduate text, advanced calculus geometric view


Dados da editora

Autor: James J. Callahan
Título: Undergraduate Texts in Mathematics; Advanced Calculus - A Geometric View
Editora: Springer; Springer US
526 Páginas
Ano de publicação: 2010-09-17
New York; NY; US
Impresso / Feito em
Peso: 2,550 kg
Língua: Inglês
69,50 € (DE)
71,45 € (AT)
93,68 CHF (CH)
POD
XVI, 526 p.

BB; Real Functions; 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; Analysis; Applications of Mathematics; Approximations and Expansions; Real Functions; Analysis; Applications of Mathematics; Approximations and Expansions; 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

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