9780130415318

Vector Calculus

by
  • ISBN13:

    9780130415318

  • ISBN10:

    0130415316

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 1/1/2002
  • Publisher: Pearson College Div
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Summary

Appropriate for sophomore-level courses in Multivariable Calculus. A traditional and accessible calculus text with a strong conceptual and geometric slant that assumes a background in single-variable calculus. The text uses the language and notation of vectors and matrices to clarify issues in multivariable calculus. It is designed to provide a greater challenge than the multivariable material typically found in the last four or five chapters of a three-semester calculus text. This challenge is balanced by clear and expansive writing and an interesting selection of material.

Table of Contents

Preface ix
Vectors
1(83)
Vectors in Two and Three Dimensions
1(8)
More About Vectors
9(11)
The Dot Product
20(9)
The Cross Product
29(14)
Equations for Planes: Distance Problems
43(9)
Some n-dimensional Geometry
52(14)
New Coordinate Systems
66(11)
Miscellaneous Exercises for Chapter 1
77(7)
Differentiation in Several Variables
84(100)
Functions of Several Variables; Graphing Surfaces
84(16)
Limits
100(16)
The Derivative
116(18)
Properties; Higher-order Partial Derivatives
134(9)
The Chain Rule
143(15)
Directional Derivatives and the Gradient
158(18)
Miscellaneous Exercises for Chapter 2
176(8)
Vector-Valued Functions
184(54)
Parametrized Curves and Kepler's Laws
184(13)
Arclength and Differential Geometry
197(19)
Vector Fields: An Introduction
216(6)
Gradient, Divergence, Curl, and the Del Operator
222(9)
Miscellaneous Exercises for Chapter 3
231(7)
Maxima and Minima in Several Variables
238(61)
Differentials and Taylor's Theorem
238(16)
Extrema of Functions
254(14)
Lagrange Multipliers
268(13)
Some Applications of Extrema
281(13)
Miscellaneous Exercises for Chapter 4
294(5)
Multiple Integration
299(78)
Introduction: Areas and Volumes
299(3)
Double Integrals
302(18)
Changing the Order of Integration
320(4)
Triple Integrals
324(10)
Change of Variables
334(22)
Applications of Integration
356(15)
Miscellaneous Exercises for Chapter 5
371(6)
Line Integrals
377(38)
Scalar and Vector Line Integrals
377(14)
Green's Theorem
391(9)
Conservative Vector Fields
400(10)
Miscellaneous Exercises for Chapter 6
410(5)
Surface Integrals and Vector Analysis
415(74)
Parametrized Surfaces
415(15)
Surface Integrals
430(19)
Stokes's and Gauss's Theorems
449(21)
Further Vector Analysis; Maxwell's Equations
470(14)
Miscellaneous Exercises for Chapter 7
484(5)
Vector Analysis in Higher Dimensions
489(34)
An Introduction to Differential Forms
489(6)
Manifolds and Integrals of k-forms
495(16)
The Generalized Stokes's Theorem
511(9)
Miscellaneous Exercises for Chapter 8
520(3)
Suggestions for Further Reading 523(2)
Answers to Selected Exercises 525(28)
Index 553

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