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Multivariable Calculus,9780534393601
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Multivariable Calculus

by
Edition:
5th
ISBN13:

9780534393601

ISBN10:
0534393608
Media:
Paperback
Pub. Date:
7/9/2003
Publisher(s):
Brooks Cole
List Price: $61.00
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Table of Contents

Parametric Equations and Polar Coordinates
1(46)
Curves Defined by Parametric Equations
1(5)
Calculus with Parametric Curves
6(8)
Polar Coordinates
14(9)
Areas and Lengths in Polar Coordinates
23(7)
Conic Sections
30(4)
Conic Sections in Polar Coordinates
34(13)
Review
37(8)
Problems Plus
45(2)
Infinite Sequences and Series
47
Sequences
47(5)
Series
52(6)
The Integral Test and Estimates of Sums
58(4)
The Comparison Tests
62(2)
Alternating Series
64(3)
Absolute Convergence and the Ratio and Root Tests
67(3)
Strategy for Testing Series
70(2)
Power Series
72(3)
Representations of Functions as Power Series
75(5)
Taylor and Maclaurin Series
80(7)
The Binomial Series
87(4)
Applications of Taylor Polynomials
91
Review
98(7)
Problems Plus
105
Vectors and the Geometry of Space
11(136)
Three-Dimensional Coordinate Systems
111(3)
Vectors
114(3)
The Dot Product
117(4)
The Cross Product
121(4)
Equations of Lines and Planes
125(4)
Cylinders and Quadric Surfaces
129(5)
Cylindrical and Spherical Coordinates
134(13)
Review
137(6)
Problems Plus
143(4)
Vector Functions
147(26)
Vector Functions and Space Curves
147(4)
Derivatives and Integrals of Vector Functions
151(4)
Arc Length and Curvature
155(6)
Motion in Space: Velocity and Acceleration
161(12)
Review
165(4)
Problems Plus
169(4)
Partial Derivatives
173(60)
Functions of Several Variables
173(9)
Limits and Continuity
182(2)
Partial Derivatives
184(8)
Tangent Planes and Linear Approximations
192(3)
The Chain Rule
195(5)
Directional Derivatives and the Gradient Vector
200(6)
Maximum and Minimum Values
206(8)
Lagrange Multipliers
214(19)
Review
219(10)
Problems Plus
229(4)
Multiple Integrals
233(44)
Double Integrals over Rectangles
233(2)
Iterated Integrals
235(2)
Double Integrals over General Regions
237(5)
Double Integrals in Polar Coordinates
242(3)
Applications of Double Integrals
245(5)
Surface Area
250(2)
Triple Integrals
252(8)
Triple Integrals in Cylindrical and Spherical Coordinates
260(4)
Change of Variables in Multiple Integrals
264(13)
Review
267(8)
Problems Plus
275(2)
Vector Calculus
277(38)
Vector Fields
277(2)
Line Integrals
279(4)
The Fundamental Theorem for Line Integrals
283(3)
Green's Theorem
286(3)
Curl and Divergence
289(4)
Parametric Surfaces and Their Areas
293(6)
Surface Integrals
299(4)
Stokes' Theorem
303(3)
The Divergence Theorem
306(9)
Review
308(5)
Problems Plus
313(2)
Second-Order Differential Equations
315(12)
Second-Order Linear Equations
315(1)
Nonhomogeneous Linear Equations
316(3)
Applications of Second-Order Differential Equations
319(2)
Series Solutions
321(6)
Review
323(4)
APPENDIX
G Complex Numbers
327


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