Stewart's Multivariable Calculus

by STEWART

• ISBN13: 9780534393588
• ISBN10: 0534393586
• Edition: 5th
• Format: Paperback
• Copyright: 2003-05-12
• Publisher: Brooks Cole

Summary

Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS, Sixth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!

Table of Contents

11 Parametric Equations and Polar Coordinates
11.1 Curves Defined by Parametric Equations	2	(4)
11.2 Calculus with Parametric Curves	6	(6)
11.3 Polar Coordinates	12	(7)
11.4 Areas and Lengths in Polar Coordinates	19	(3)
11.5 Conic sections	22	(4)
11.6 Conic Sections in Polar Coordinates	26	(3)
Technology Plus	29	(3)
12 Infinite sequences and series
12.1 Sequences	32	(5)
12.2 Series	37	(4)
12.3 The Integral Test and Estimates of Sums	41	(3)
12.4 The Comparison Tests	44	(3)
12.5 Alternating series	47	(3)
12.6 Absolute Convergence and the Ratio and Root Tests	50	(6)
12.7 Strategy for Testing series	56	(2)
12.8 Power series	58	(3)
12.9 Representations of Functions as Power Series	61	(4)
12.10 Taylor and Maclaurin Series	65	(7)
12.11 The Binomial Series	72	(2)
12.12 Applications of Taylor Polynomials	74	(4)
Technology Plus	78	(4)
13 Vectors and the Geometry of Space
13.1 Three-Dimensional Coordinate systems	82	(4)
13.2 Vectors	86	(6)
13.3 The Dot Product	92	(4)
13.4 The Cross Product	96	(4)
13.5 Equations of Lines and Planes	100	(5)
13.6 Cylinders and Quadric Surfaces	105	(6)
13.7 Cylindrical and Spherical Coordinates	111	(3)
Technology Plus	114	(4)
14 Vector Functions
14.1 Vector Functions and Space Curves	118	(3)
14.2 Derivatives and Integrals of Vector Functions	121	(3)
14.3 Arc Length and Curvature	124	(5)
14.4 Motion in Space: Velocity and Acceleration	129	(4)
Technology Plus	133	(3)
15 Partial Derivatives
15.1 Functions of Several Variables	136	(4)
15.2 Limits and Continuity	140	(3)
15.3 Partial Derivatives	143	(3)
15.4 Tangent Planes and Linear Approximations	146	(3)
15.5 The Chain Rule	149	(2)
15.6 Directional Derivatives and the Gradient Vector	151	(3)
15.7 Maximum and Minimum Values	154	(8)
15.8 Lagrange Multipliers 159
Technology Plus	162	(4)
16 Multiple Integrals
16.1 Double integrals over Rectangles	166	(4)
16.2 Iterated integrals	170	(3)
16.3 Double Integrals over General Regions	173	(5)
16.4 Double Integrals over Polar Coordinates	178	(3)
16.5 Applications of Double Integrals	181	(4)
16.6 Surface Area	185	(2)
16.7 Triple Integrals	187	(5)
16.8 Triple Integrals in Cylindrical and Spherical Coordinates	192	(3)
16.9 Change of Variables in Multiple Integrals	195	(4)
Technology Plus	199	(3)
17 Vector Calculus
17.1 Vector Fields	202	(3)
17.2 Line Integrals	205	(5)
17.3 The Fundamental Theorem for Line Integrals	210	(4)
17.4 Green's Theorem	214	(3)
17.5 Curl and Divergence	217	(4)
17.6 Parametric Surfaces and Their Areas	221	(5)
17.7 Surface Integrals	226	(4)
17.8 Stokes' Theorem	230	(2)
17.9 The Divergence Theorem	232	(2)
Technology Plus	234	(4)
18 Second-Order Differential Equations
18.1 Second Order Linear Equations	238	(4)
18.2 Nonhomogeneous Linear Equations	242	(3)
18.3 Applications of Second Order Differential Equations	245	(2)
18.4 Series solutions	247	(3)
Technology Plus	250	(1)
On Your Own
Chapter 11 On Your Own	251	(7)
Chapter 12 On Your Own	258	(12)
Chapter 13 On Your Own	270	(7)
Chapter 14 On Your Own	277	(4)
Chapter 15 On Your Own	281	(8)
Chapter 16 On Your Own	289	(9)
Chapter 17 On Your Own	298	(9)
Chapter 18 On Your Own	307	(4)
Answers to On Your Own	311
046500721X
List of Maps	xi
Preface: Another American Way of War	xiii
PART ONE: COMMERCIAL POWER
1 "To Conquer Upon the Sea": Barbary Wars, 1801-1805, 1815	3	(27)
2 "Butcher and Bolt": From the Marquesas, 1813, to China, 1859	30	(26)
3 Empire Emerging: From Korea, 1871, to Samoa, 1899	56	(13)
PART TWO: GREAT POWER
4 Red Summer: Boxer Uprising, 1900	69	(30)
5 "Attraction" and "Chastisement": The Philippine War, 1899-1902	99	(30)
6 Caribbean Constabulary: Cuba, Panama, Nicaragua, Mexico, 1898-1914	129	(27)
7 Lords of Hispaniola: Haiti, 1915-1934; Dominican Republic, 1916-1924	156	(26)
8 The Dusty Trail: The Pancho Villa Punitive Expedition, 1916-1917	182	(23)
9 Blood on the Snow: Russia, 1918-1920	205	(30)
10 Chasing Sandino: Nicaragua, 1926-1933	235	(18)
11 "By Bluff Alone": China, 1901-1941	253	(28)
PART THREE: SUPERPOWER 12 Lessons Learned: The Small Wars Manual	281	(72)
13 Lessons Unlearned: Vietnam, 1959-1975	286	(32)
14 In the Shadow of Vietnam: The Powell Doctrine and Small Wars in the 1990'S	318	(18)
15 In Defense of the Pax Americana: Small Wars in the Twenty-First Century	336	(17)
Notes	353	(34)
Bibliography	387	(22)
Acknowledgments	409	(2)
Index	411