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Vector Calculus,9780131858749
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Vector Calculus

by
Edition:
3rd
ISBN13:

9780131858749

ISBN10:
0131858742
Format:
Hardcover
Pub. Date:
3/16/2005
Publisher(s):
Pearson
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Summary

This text uses the language and notation of vectors and matrices to clarify issues in multivariable calculus. Accessible to anyone with a good background in single-variable calculus, it presents more linear algebra than usually found in a multivariable calculus book. Colley balances this with very clear and expansive exposition, many figures, and numerous, wide-ranging exercises. Instructors will appreciate Colleyrs"s writing style, mathematical precision, level of rigor, and full selection of topics treated. Vectors:Vectors in Two and Three Dimensions. More About Vectors. The Dot Product. The Cross Product. Equations for Planes; Distance Problems. Somen-Dimensional Geometry. New Coordinate Systems.Differentiation in Several Variables:Functions of Several Variables; Graphing Surfaces. Limits. The Derivative. Properties; Higher-Order Partial Derivatives; Newtonrs"s Method. The Chain Rule. Directional Derivatives and the Gradient.Vector-Valued Functions:Parametrized Curves and Kepler's Laws. Arclength and Differential Geometry. Vector Fields: An Introduction. Gradient, Divergence, Curl, and the Del Operator.Maxima and Minima in Several Variables:Differentials and Taylor's Theorem. Extrema of Functions. Lagrange Multipliers. Some Applications of Extrema.Multiple Integration:Introduction: Areas and Volumes. Double Integrals. Changing the Order of Integration. Triple Integrals. Change of Variables. Applications of Integration.Line Integrals:Scalar and Vector Line Integrals. Green's Theorem. Conservative Vector Fields.Surface Integrals and Vector Analysis:Parametrized Surfaces. Surface Integrals. Stokes's and Gauss's Theorems. Further Vector Analysis; Maxwell's Equations.Vector Analysis in Higher Dimensions:An Introduction to Differential Forms. Manifolds and Integrals ofk-forms. The Generalized Stokes's Theorem. For all readers interested in multivariable calculus.

Author Biography

Susan Colley is the Andrew and Pauline Delaney Professor of Mathematics at Oberlin College and currently Chair of the Department, having also previously served as Chair. She received S.B. and Ph.D. degrees in mathematics from the Massachusetts Institute of Technology prior to joining the faculty at Oberlin in 1983. Her research focuses on enumerative problems in algebraic geometry, particularly concerning multiple-point singularities and higher-order contact of plane curves. Professor Colley has published papers on algebraic geometry and commutative algebra, as well as articles on other mathematical subjects. She has lectured internationally on her research and has taught a wide range of subjects in undergraduate mathematics. Professor Colley is a member of several professional and honorary societies, including the American Mathematical Society, the Mathematical Association of America, Phi Beta Kappa, and Sigma Xi.

Table of Contents

Preface ix
To the Student: Some Preliminary Notation xiii
Vectors
1(78)
Vectors in Two and Three Dimensions
1(7)
More About Vectors
8(10)
The Dot Product
18(9)
The Cross Product
27(12)
Equations for Planes; Distance Problems
39(8)
Some n-dimensional Geometry
47(14)
New Coordinate Systems
61(11)
True/False Exercises for Chapter 1
72(1)
Miscellaneous Exercises for Chapter 1
73(6)
Differentiation in Several Variables
79(98)
Functions of Several Variables; Graphing Surfaces
79(14)
Limits
93(15)
The Derivative
108(17)
Properties; Higher-order Partial Derivatives; Newton's Method
125(14)
The Chain Rule
139(14)
Directional Derivatives and the Gradient
153(17)
True/False Exercises for Chapter 2
170(1)
Miscellaneous Exercises for Chapter 2
171(6)
Vector-Valued Functions
177(53)
Parametrized Curves and Kepler's Laws
177(13)
Arclength and Differential Geometry
190(18)
Vector Fields: An Introduction
208(6)
Gradient, Divergence, Curl, and the Del Operator
214(9)
True/False Exercises for Chapter 3
223(1)
Miscellaneous Exercises for Chapter 3
223(7)
Maxima and Minima in Several Variables
230(59)
Differentials and Taylor's Theorem
230(15)
Extrema of Functions
245(14)
Lagrange Multipliers
259(14)
Some Applications of Extrema
273(11)
True/False Exercises for Chapter 4
284(1)
Miscellaneous Exercises for Chapter 4
285(4)
Multiple Integration
289(74)
Introduction: Areas and Volumes
289(3)
Double Integrals
292(17)
Changing the Order of Integration
309(3)
Triple Integrals
312(10)
Change of Variables
322(21)
Applications of Integration
343(14)
True/False Exercises for Chapter 5
357(1)
Miscellaneous Exercises for Chapter 5
358(5)
Line Integrals
363(42)
Scalar and Vector Line Integrals
363(18)
Green's Theorem
381(9)
Conservative Vector Fields
390(10)
True/False Exercises for Chapter 6
400(1)
Miscellaneous Exercises for Chapter 6
401(4)
Surface Integrals and Vector Analysis
405(72)
Parametrized Surfaces
405(14)
Surface Integrals
419(20)
Stokes's and Gauss's Theorems
439(18)
Further Vector Analysis; Maxwell's Equations
457(12)
True/False Exercises for Chapter 7
469(1)
Miscellaneous Exercises for Chapter 7
470(7)
Vector Analysis in Higher Dimensions
477(32)
An Introduction to Differential Forms
477(6)
Manifolds and Integrals of k-forms
483(15)
The Generalized Stokes's Theorem
498(8)
True/False Exercises for Chapter 8
506(1)
Miscellaneous Exercises for Chapter 8
507(2)
Suggestions for Further Reading 509(2)
Answers to Selected Exercises 511(32)
Index 543


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