11 Parametric Equations and Polar Coordinates 


11.1 Curves Defined by Parametric Equations 


2  (4) 

11.2 Calculus with Parametric Curves 


6  (6) 


12  (7) 

11.4 Areas and Lengths in Polar Coordinates 


19  (3) 


22  (4) 

11.6 Conic Sections in Polar Coordinates 


26  (3) 


29  (3) 
12 Infinite sequences and series 



32  (5) 


37  (4) 

12.3 The Integral Test and Estimates of Sums 


41  (3) 

12.4 The Comparison Tests 


44  (3) 


47  (3) 

12.6 Absolute Convergence and the Ratio and Root Tests 


50  (6) 

12.7 Strategy for Testing series 


56  (2) 


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) 


78  (4) 
13 Vectors and the Geometry of Space 


13.1 ThreeDimensional Coordinate systems 


82  (4) 


86  (6) 


92  (4) 


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) 


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) 


133  (3) 
15 Partial Derivatives 


15.1 Functions of Several Variables 


136  (4) 

15.2 Limits and Continuity 


140  (3) 


143  (3) 

15.4 Tangent Planes and Linear Approximations 


146  (3) 


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) 


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) 


185  (2) 


187  (5) 

16.8 Triple Integrals in Cylindrical and Spherical Coordinates 


192  (3) 

16.9 Change of Variables in Multiple Integrals 


195  (4) 


199  (3) 
17 Vector Calculus 



202  (3) 


205  (5) 

17.3 The Fundamental Theorem for Line Integrals 


210  (4) 


214  (3) 


217  (4) 

17.6 Parametric Surfaces and Their Areas 


221  (5) 


226  (4) 


230  (2) 

17.9 The Divergence Theorem 


232  (2) 


234  (4) 
18 SecondOrder 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) 


247  (3) 


250  (1) 
On Your Own 



251  (7) 


258  (12) 


270  (7) 


277  (4) 


281  (8) 


289  (9) 


298  (9) 


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, 18011805, 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, 18991902 


99  (30) 

6 Caribbean Constabulary: Cuba, Panama, Nicaragua, Mexico, 18981914 


129  (27) 

7 Lords of Hispaniola: Haiti, 19151934; Dominican Republic, 19161924 


156  (26) 

8 The Dusty Trail: The Pancho Villa Punitive Expedition, 19161917 


182  (23) 

9 Blood on the Snow: Russia, 19181920 


205  (30) 

10 Chasing Sandino: Nicaragua, 19261933 


235  (18) 

11 "By Bluff Alone": China, 19011941 


253  (28) 
PART THREE: SUPERPOWER 12 Lessons Learned: The Small Wars Manual 

281  (72) 

13 Lessons Unlearned: Vietnam, 19591975 


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 TwentyFirst Century 


336  (17) 
Notes 

353  (34) 
Bibliography 

387  (22) 
Acknowledgments 

409  (2) 
Index 

411  