Preface 

vii  

Parametric Equations and Polar Coordinates 


686  (50) 

Curves Defined by Parametric Equations 


687  (9) 

Laboratory Project Running Circles around Circles 


695  (1) 

Calculus with Parametric Curves 


696  (9) 

Laboratory Project Bezier Curves 


705  (1) 


705  (10) 

Areas and Lengths in Polar Coordinates 


715  (5) 


720  (8) 

Conic Sections in Polar Coordinates 


728  (8) 


732  (3) 


735  (1) 

Infinite Sequences and Series 


736  (92) 


737  (12) 

Laboratory Project Logistic Sequences 


749  (1) 


749  (10) 

The Integral Test and Estimates of Sums 


759  (7) 


766  (5) 


771  (5) 

Absolute Convergence and the Ratio and Root Tests 


776  (7) 

Strategy for Testing Series 


783  (2) 


785  (5) 

Representations of Functions as Power Series 


790  (6) 

Taylor and Maclaurin Series 


796  (12) 

Laboratory Project An Elusive Limit 


808  (1) 


808  (4) 

Writing Project How Newton Discovered the Binomial Series 


812  (1) 

Applications of Taylor Polynomials 


812  (16) 

Applied Project Radiation from the Stars 


875  


822  (3) 


825  (3) 

Vectors and the Geometry of Space 


828  (56) 

ThreeDimensional Coordinate Systems 


829  (5) 


834  (9) 


843  (7) 


850  (8) 

Discovery Project The Geometry of a Tetrahedron 


858  (1) 

Equations of Lines and Planes 


858  (10) 

Laboratory Project Putting 3D in Perspective 


868  (1) 

Cylinders and Quadric Surfaces 


868  (7) 

Cylindrical and Spherical Coordinates 


875  (9) 

Laboratory Project Families of Surfaces 


880  (1) 


880  (3) 


883  (1) 


884  (38) 

Vector Functions and Space Curves 


885  (7) 

Derivatives and Integrals of Vector Functions 


892  (6) 


898  (8) 

Motion in Space: Velocity and Acceleration 


906  (16) 

Applied Project Kepler's Laws 


916  (1) 


917  (3) 


920  (2) 


922  (94) 

Functions of Several Variables 


923  (15) 


938  (7) 


945  (14) 

Tangent Planes and Linear Approximations 


959  (8) 


967  (9) 

Directional Derivatives and the Gradient Vector 


976  (13) 

Maximum and Minimum Values 


989  (12) 

Applied Project Designing a Dumpster 


999  (1) 

Discovery Project Quadratic Approximations and Critical Points 


1000  (1) 


1001  (15) 

Applied Project Rocket Science 


1008  (1) 

Applied Project HydroTurbine Optimization 


1009  (1) 


1010  (4) 


1014  (2) 


1016  (74) 

Double Integrals over Rectangles 


1017  (8) 


1025  (6) 

Double Integrals over General Regions 


1031  (8) 

Double Integrals in Polar Coordinates 


1039  (6) 

Applications of Double Integrals 


1045  (10) 


1055  (4) 


1059  (10) 

Discovery Project Volumes of Hyperspheres 


1068  (1) 

Triple Integrals in Cylindrical and Spherical Coordinates 


1069  (8) 

Applied Project Roller Derby 


1075  (1) 

Discovery Project The Intersection of Three Cylinders 


1076  (1) 

Change of Variables in Multiple Integrals 


1077  (13) 


1085  (3) 


1088  (2) 


1090  (86) 


1091  (7) 


1098  (12) 

The Fundamental Theorem for Line Integrals 


1110  (9) 


1119  (7) 


1126  (8) 

Parametric Surfaces and Their Areas 


1134  (11) 


1145  (12) 


1157  (6) 

Writing Project Three Men and Two Theorems 


1162  (1) 


1163  (7) 


1170  (6) 


1171  (3) 


1174  (2) 

SecondOrder Differential Equations 


1176  (1) 

SecondOrder Linear Equations 


1177  (6) 

Nonhomogeneous Linear Equations 


1183  (8) 

Applications of SecondOrder Differential Equations 


1191  (8) 


1199  (4) 


1203  
Appendixes 

1  (42) 


2  (3) 


5  (8) 

H Answers to OddNumbered Exercises 


13  (30) 
Index 

43  