Multivariable Calculus

by STEWART

• ISBN13: 9780534393601
• ISBN10: 0534393608
• Edition: 5th
• Format: Paperback
• Copyright: 2003-07-09
• Publisher: Brooks Cole

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