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Vector Calculus

ISBN: 9780131492042 | 0131492047
Edition: 1st
Format: Hardcover
Publisher: Unknown
Pub. Date: 8/1/1997

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SummaryTable of Contents
A traditional and very well written, accessible calculus text with a strong conceptual and geometric slant. Starts with linear algebra as a tool set and ends with an easy presentation of differential forms.
Prefacevii
1 Vectors
1(83)
1.1 Vectors in Two and Three Dimensions
1(9)
... MORE
1.2 More About Vectors
10(11)
1.3 The Dot Product
21(8)
1.4 The Cross Product
29(15)
1.5 Equations for Planes; Distance Problems
44(9)
1.6 Some n-Dimensional Geometry
53(14)
1.7 New Coordinate Systems
67(12)
1.8 Miscellaneous Exercises for Chapter 1
79(5)
2 Differentiation in Several Variables
84(93)
2.1 Functions of Several Variables; Graphing Surfaces
84(16)
2.2 Limits
100(17)
2.3 The Derivative
117(17)
2.4 Properties; Higher-order Partial Derivatives
134(10)
2.5 The Chain Rule
144(14)
2.6 Directional Derivatives and the Gradient
158(14)
2.7 Miscellaneous Exercises for Chapter 2
172(5)
3 Vector-Valued Functions
177(53)
3.1 Parametrized Curves and Kepler's Laws
177(13)
3.2 Arclength and Differential Geometry
190(20)
3.3 Vector Fields: An Introduction
210(6)
3.4 Gradient, Divergence, Curl, and the Del Operator
216(10)
3.5 Miscellaneous Exercises for Chapter 3
226(4)
4 Maxima and Minima in Several Variables
230(58)
4.1 Differentials and Taylor's Theorem
230(17)
4.2 Extrema of Functions
247(11)
4.3 Lagrange Multipliers
258(13)
4.4 Some Applications of Extrema
271(14)
4.5 Miscellaneous Exercises for Chapter 4
285(3)
5 Multiple Integration
288(83)
5.1 Introduction: Areas and Volumes
288(4)
5.2 Double Integrals
292(19)
5.3 Changing the Order of Integration
311(3)
5.4 Triple Integrals
314(12)
5.5 Change of Variables
326(24)
5.6 Applications of Integration
350(15)
5.7 Miscellaneous Exercises for Chapter 5
365(6)
6 Line Integrals
371(40)
6.1 Scalar and Vector Line Integrals
371(14)
6.2 Green's Theorem
385(10)
6.3 Conservative Vector Fields
395(11)
6.4 Miscellaneous Exercises for Chapter 6
406(5)
7 Surface Integrals and Vector Analysis
411(94)
7.1 Parametrized Surfaces
411(16)
7.2 Surface Integrals
427(21)
7.3 Stokes's and Gauss's Theorems
448(21)
7.4 Further Vector Analysis; Maxwell's Equations
469(14)
7.5 An Introduction to Differential Forms
483(16)
7.6 Miscellaneous Exercises for Chapter 7
499(6)
Suggestions for Further Reading505(2)
Answers to Selected Exercises507(21)
Index528

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