Preface 

xi  

Parametric Equations and Polar Coordinates 


650  (50) 

Curves Defined by Parametric Equations 


651  (9) 

Laboratory Project Running Circles around Circles 


659  (1) 

Calculus with Parametric Curves 


660  (9) 

Laboratory Project Bezier Curves 


669  (1) 


669  (10) 

Areas and Lengths in Polar Coordinates 


679  (5) 


684  (8) 

Conic Sections in Polar Coordinates 


692  (8) 


696  (3) 


699  (1) 

Infinite Sequences and Series 


700  (92) 


701  (12) 

Laboratory Project Logistic Sequences 


713  (1) 


713  (10) 

The Integral Test and Estimates of Sums 


723  (7) 


730  (5) 


735  (5) 

Absolute Convergence and the Ratio and Root Tests 


740  (7) 

Strategy for Testing Series 


747  (2) 


749  (5) 

Representations of Functions as Power Series 


754  (6) 

Taylor and Maclaurin Series 


760  (12) 

Laboratory Project An Elusive Limit 


772  (1) 


772  (4) 

Writing Project How Newton Discovered the Binomial Series 


776  (1) 

Applications of Taylor Polynomials 


776  (16) 

Applied Project Radiation from the Stars 


785  (1) 


786  (3) 


789  (3) 

Vectors and the Geometry of Space 


792  (56) 

ThreeDimensional Coordinate Systems 


793  (5) 


798  (9) 


807  (7) 


814  (8) 

Discovery Project  The Geometry of a Tetrahedron 


822  (1) 

Equations of Lines and Planes 


822  (10) 

Laboratory Project Putting 3D in Perspective 


832  (1) 

Cylinders and Quadric Surfaces 


832  (7) 

Cylindrical and Spherical Coordinates 


839  (9) 

Laboratory Project Families of Surfaces 


844  (1) 


844  (3) 


847  (1) 


848  (38) 

Vector Functions and Space Curves 


849  (7) 

Derivatives and Integrals of Vector Functions 


856  (6) 


862  (8) 

Motion in Space: Velocity and Acceleration 


870  (16) 

Applied Project Kepler's Laws 


880  (1) 


881  (3) 


884  (2) 


886  (94) 

Functions of Several Variables 


887  (15) 


902  (7) 


909  (14) 

Tangent Planes and Linear Approximations 


923  (8) 


931  (9) 

Directional Derivatives and the Gradient Vector 


940  (13) 

Maximum and Minimum Values 


953  (12) 

Applied Project Designing a Dumpster 


963  (1) 

Discovery Project Quadratic Approximations and Critical Points 


964  (1) 


965  (15) 

Applied Project Rocket Science 


972  (1) 

Applied Project HydroTurbine Optimization 


973  (1) 


974  (4) 


978  (2) 


980  (74) 

Double Integrals over Rectangles 


981  (8) 


989  (6) 

Double Integrals over General Regions 


995  (8) 

Double Integrals in Polar Coordinates 


1003  (6) 

Applications of Double Integrals 


1009  (10) 


1019  (4) 


1023  (10) 

Discovery Project Volumes of Hyperspheres 


1032  (1) 

Triple Integrals in Cylindrical and Spherical Coordinates 


1033  (8) 

Applied Project  Roller Derby 


1039  (1) 

Discovery Project  The Intersection of Three Cylinders 


1040  (1) 

Change of Variables in Multiple Integrals 


1041  (13) 


1049  (3) 


1052  (2) 


1054  (86) 


1055  (7) 


1062  (12) 

The Fundamental Theorem for Line Integrals 


1074  (9) 


1083  (7) 


1090  (8) 

Parametric Surfaces and Their Areas 


1098  (11) 


1109  (12) 


1121  (6) 

Writing Project Three Men and Two Theorems 


1126  (1) 


1127  (7) 


1134  (6) 


1135  (3) 


1138  (2) 

SecondOrder Differential Equations 


1140  (1) 

SecondOrder Linear Equations 


1141  (6) 

Nonhomogeneous Linear Equations 


1147  (8) 

Applications of SecondOrder Differential Equations 


1155  (8) 


1163  (4) 


1167  


1  (42) 


2  (3) 


5  (8) 

H Answers to OddNumbered Exercises 


13  (30) 
Index 

43  