Language: English
Pages: 380
Preface......Page 4
Outline......Page 6
Introduction......Page 10
Integration by Parts......Page 12
Integrals Involving Trig Functions......Page 22
Trig Substitutions......Page 32
Partial Fractions......Page 43
Integrals Involving Roots......Page 51
Integrals Involving Quadratics......Page 53
Using Integral Tables......Page 61
Integration Strategy......Page 64
Improper Integrals......Page 71
Comparison Test for Improper Integrals......Page 78
Approximating Definite Integrals......Page 85
Introduction......Page 92
Arc Length......Page 93
Surface Area......Page 99
Center of Mass......Page 105
Hydrostatic Pressure and Force......Page 109
Probability......Page 114
Introduction......Page 118
Parametric Equations and Curves......Page 119
Tangents with Parametric Equations......Page 130
Area with Parametric Equations......Page 137
Arc Length with Parametric Equations......Page 140
Surface Area with Parametric Equations......Page 144
Polar Coordinates......Page 146
Tangents with Polar Coordinates......Page 156
Area with Polar Coordinates......Page 158
Arc Length with Polar Coordinates......Page 165
Surface Area with Polar Coordinates......Page 167
Arc Length and Surface Area Revisited......Page 168
Introduction......Page 170
Sequences......Page 172
More on Sequences......Page 182
Series – The Basics......Page 188
Series – Convergence/Divergence......Page 194
Series – Special Series......Page 203
Integral Test......Page 211
Comparison Test / Limit Comparison Test......Page 220
Alternating Series Test......Page 229
Absolute Convergence......Page 235
Ratio Test......Page 239
Root Test......Page 246
Strategy for Series......Page 249
Estimating the Value of a Series......Page 252
Power Series......Page 263
Power Series and Functions......Page 271
Taylor Series......Page 278
Applications of Series......Page 288
Binomial Series......Page 293
Introduction......Page 295
Vectors – The Basics......Page 296
Vector Arithmetic......Page 300
Dot Product......Page 305
Cross Product......Page 313
Introduction......Page 319
The 3-D Coordinate System......Page 321
Equations of Lines......Page 327
Equations of Planes......Page 333
Quadric Surfaces......Page 336
Functions of Several Variables......Page 342
Vector Functions......Page 349
Calculus with Vector Functions......Page 358
Tangent, Normal and Binormal Vectors......Page 361
Arc Length with Vector Functions......Page 365
Curvature......Page 368
Velocity and Acceleration......Page 370
Cylindrical Coordinates......Page 373
Spherical Coordinates......Page 375
