| Preface |
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vii | |
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Parametric Equations and Polar Coordinates |
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686 | (50) |
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Curves Defined by Parametric Equations |
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687 | (9) |
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Laboratory Project Running Circles around Circles |
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695 | (1) |
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Calculus with Parametric Curves |
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696 | (9) |
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Laboratory Project Bezier Curves |
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705 | (1) |
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705 | (10) |
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Areas and Lengths in Polar Coordinates |
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715 | (5) |
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720 | (8) |
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Conic Sections in Polar Coordinates |
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728 | (8) |
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732 | (3) |
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735 | (1) |
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Infinite Sequences and Series |
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736 | (92) |
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737 | (12) |
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Laboratory Project Logistic Sequences |
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749 | (1) |
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749 | (10) |
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The Integral Test and Estimates of Sums |
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759 | (7) |
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766 | (5) |
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771 | (5) |
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Absolute Convergence and the Ratio and Root Tests |
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776 | (7) |
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Strategy for Testing Series |
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783 | (2) |
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785 | (5) |
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Representations of Functions as Power Series |
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790 | (6) |
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Taylor and Maclaurin Series |
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796 | (12) |
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Laboratory Project An Elusive Limit |
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808 | (1) |
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808 | (4) |
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Writing Project How Newton Discovered the Binomial Series |
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812 | (1) |
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Applications of Taylor Polynomials |
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812 | (16) |
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Applied Project Radiation from the Stars |
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875 | |
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822 | (3) |
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825 | (3) |
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Vectors and the Geometry of Space |
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828 | (56) |
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Three-Dimensional Coordinate Systems |
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829 | (5) |
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834 | (9) |
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843 | (7) |
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850 | (8) |
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Discovery Project The Geometry of a Tetrahedron |
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858 | (1) |
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Equations of Lines and Planes |
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858 | (10) |
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Laboratory Project Putting 3D in Perspective |
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868 | (1) |
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Cylinders and Quadric Surfaces |
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868 | (7) |
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Cylindrical and Spherical Coordinates |
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875 | (9) |
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Laboratory Project Families of Surfaces |
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880 | (1) |
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880 | (3) |
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883 | (1) |
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884 | (38) |
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Vector Functions and Space Curves |
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885 | (7) |
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Derivatives and Integrals of Vector Functions |
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892 | (6) |
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898 | (8) |
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Motion in Space: Velocity and Acceleration |
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906 | (16) |
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Applied Project Kepler's Laws |
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916 | (1) |
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917 | (3) |
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920 | (2) |
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922 | (94) |
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Functions of Several Variables |
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923 | (15) |
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938 | (7) |
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945 | (14) |
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Tangent Planes and Linear Approximations |
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959 | (8) |
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967 | (9) |
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Directional Derivatives and the Gradient Vector |
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976 | (13) |
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Maximum and Minimum Values |
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989 | (12) |
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Applied Project Designing a Dumpster |
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999 | (1) |
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Discovery Project Quadratic Approximations and Critical Points |
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1000 | (1) |
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1001 | (15) |
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Applied Project Rocket Science |
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1008 | (1) |
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Applied Project Hydro-Turbine Optimization |
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1009 | (1) |
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1010 | (4) |
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1014 | (2) |
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1016 | (74) |
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Double Integrals over Rectangles |
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1017 | (8) |
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1025 | (6) |
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Double Integrals over General Regions |
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1031 | (8) |
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Double Integrals in Polar Coordinates |
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1039 | (6) |
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Applications of Double Integrals |
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1045 | (10) |
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1055 | (4) |
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1059 | (10) |
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Discovery Project Volumes of Hyperspheres |
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1068 | (1) |
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Triple Integrals in Cylindrical and Spherical Coordinates |
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1069 | (8) |
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Applied Project Roller Derby |
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1075 | (1) |
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Discovery Project The Intersection of Three Cylinders |
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1076 | (1) |
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Change of Variables in Multiple Integrals |
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1077 | (13) |
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1085 | (3) |
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1088 | (2) |
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1090 | (86) |
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1091 | (7) |
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1098 | (12) |
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The Fundamental Theorem for Line Integrals |
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1110 | (9) |
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1119 | (7) |
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1126 | (8) |
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Parametric Surfaces and Their Areas |
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1134 | (11) |
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1145 | (12) |
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1157 | (6) |
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Writing Project Three Men and Two Theorems |
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1162 | (1) |
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1163 | (7) |
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1170 | (6) |
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1171 | (3) |
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1174 | (2) |
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Second-Order Differential Equations |
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1176 | (1) |
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Second-Order Linear Equations |
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1177 | (6) |
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Nonhomogeneous Linear Equations |
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1183 | (8) |
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Applications of Second-Order Differential Equations |
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1191 | (8) |
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1199 | (4) |
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|
1203 | |
| Appendixes |
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1 | (42) |
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2 | (3) |
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5 | (8) |
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H Answers to Odd-Numbered Exercises |
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|
13 | (30) |
| Index |
|
43 | |