Schaum's outlines, Calculus

Contents......Page 9
 Linear Coordinate System......Page 15
 Finite Intervals......Page 16
 Inequalities......Page 17
 Coordinates......Page 23
 Quadrants......Page 24
 The Distance Formula......Page 25
 The Midpoint Formulas......Page 26
 Proofs of Geometric Theorems......Page 27
 The Sign of the Slope......Page 32
 Slope and Steepness......Page 33
 Equations of Lines......Page 34
 Parallel Lines......Page 35
 Perpendicular Lines......Page 36
 The Standard Equation of a Circle......Page 43
 Parabolas......Page 51
 Hyperbolas......Page 52
 Conic Sections......Page 53
Chapter 6 Functions......Page 63
 Limit of a Function......Page 70
 Infinity......Page 71
 Continuous Function......Page 80
 Notation for Derivatives......Page 87
 Differentiability......Page 88
 Differentiation......Page 93
 Alternative Formulation of the Chain Rule......Page 94
 Inverse Functions......Page 95
 Higher Derivatives......Page 96
 Derivatives of Higher Order......Page 104
Chapter 12 Tangent and Normal Lines......Page 107
 The Angles of Intersection......Page 108
 Relative Maximum and Minimum......Page 112
 Increasing and Decreasing Functions......Page 114
 Second Derivative Test for Relative Extrema......Page 119
 First Derivative Test......Page 120
 Tabular Method for Finding the Absolute Maximum and Minimum......Page 121
 Concavity......Page 133
 Symmetry......Page 134
 Hints for Sketching the Graph of y = f (x)......Page 136
 Angle Measure......Page 144
 Sine and Cosine Functions......Page 145
 Continuity of cos x and sin x......Page 153
 Graph of cos x......Page 154
 Other Relationships......Page 156
 Graph of y = tan x......Page 157
 Angles Between Curves......Page 158
 The Derivative of sin[sup(-1)] x......Page 166
 The Inverse Tangent Function......Page 167
 Rectilinear Motion......Page 175
 Motion Under the Influence of Gravity......Page 176
 Circular Motion......Page 177
Chapter 20 Related Rates......Page 181
Chapter 21 Differentials. Newton’s Method......Page 187
 The Differential......Page 188
 Newton’s Method......Page 189
 Laws for Antiderivatives......Page 195
 Area Under a Curve......Page 204
 Properties of the Definite Integral......Page 207
 Average Value of a Function on a Closed Interval......Page 212
 Change of Variable in a Definite Integral......Page 213
 The Natural Logarithm......Page 220
 Properties of the Natural Logarithm......Page 221
 Properties of e[sup(x)]......Page 228
 The General Exponential Function......Page 230
 General Logarithmic Functions......Page 231
 L’Hôpital’s Rule......Page 236
 Indeterminate Types 0[sup(0)], ∞[sup(0)], and 1[sup(∞)]......Page 237
 Half-Life......Page 244
 Area Between a Curve and the y Axis......Page 249
 Areas Between Curves......Page 250
 Arc Length......Page 251
 Disk Formula......Page 258
 Washer Method......Page 260
 Difference of Shells Formula......Page 261
 Cross-Section Formula (Slicing Formula)......Page 262
Chapter 31 Techniques of Integration I: Integration by Parts......Page 273
 Trigonometric Integrands......Page 280
 Trigonometric Substitutions......Page 282
Chapter 33 Techniques of Integration III: Integration by Partial Fractions......Page 293
 Method of Partial Fractions......Page 294
Chapter 34 Techniques of Integration IV: Miscellaneous Substitutions......Page 302
 Discontinuities of the Integrand......Page 307
Chapter 36 Applications of Integration III: Area of a Surface of Revolution......Page 315
 Parametric Equations......Page 321
 Arc Length for a Parametric Curve......Page 322
 Derivative of Arc Length......Page 326
 The Circle of Curvature......Page 327
 The Evolute......Page 328
 Sum and Difference of Two Vectors......Page 335
 Components of a Vector......Page 336
 Scalar Product (or Dot Product)......Page 337
 Differentiation of Vector Functions......Page 338
 Acceleration in Curvilinear Motion......Page 346
 Tangential and Normal Components of Acceleration......Page 347
Chapter 41 Polar Coordinates......Page 353
 Some Typical Polar Curves......Page 354
 Points of Intersection......Page 355
 Angle of Intersection......Page 356
 Curvature......Page 357
 Limit of a Sequence......Page 366
 Monotonic Sequences......Page 368
 Geometric Series......Page 374
 Series of Positive Terms......Page 380
 Alternating Series......Page 389
 Power Series......Page 397
 Uniform Convergence......Page 399
 Taylor and Maclaurin Series......Page 410
 Applications of Taylor’s Formula with Remainder......Page 412
 Limits......Page 419
 Partial Derivatives......Page 420
 Partial Derivatives of Higher Order......Page 421
 Total Differential......Page 428
 Chain Rules......Page 429
 Implicit Differentiation......Page 431
 Vectors in Space......Page 440
 Direction Cosines of a Vector......Page 441
 Vector Product of Two Vectors......Page 442
 Triple Scalar Product......Page 444
 The Straight Line......Page 445
 The Plane......Page 446
 Cylindrical Surfaces......Page 455
 Elliptic Paraboloid......Page 456
 Hyperboloid of One Sheet......Page 457
 Hyperboloid of Two Sheets......Page 458
 Tangent Plane and Normal Line to a Surface......Page 459
 Surface of Revolution......Page 460
 Directional Derivatives......Page 466
 Absolute Maximum and Minimum Values......Page 467
 Vector Differentiation......Page 474
 Space Curves......Page 475
 Surfaces......Page 476
 The Operation ∇......Page 477
 Divergence and Curl......Page 478
 Line Integrals......Page 479
 The Double Integral......Page 488
 The Iterated Integral......Page 489
 Centroids......Page 495
 Moments of Inertia......Page 496
Chapter 56 Double Integration Applied to Volume Under a Surface and the Area of a Curved Surface......Page 503
 Cylindrical and Spherical Coordinates......Page 512
 Evaluation of Triple Integrals......Page 513
 Centroids and Moments of Inertia......Page 514
Chapter 58 Masses of Variable Density......Page 524
 Integrating Factors......Page 530
 Second-Order Equations......Page 531
Appendix A......Page 541
Appendix B......Page 542
 C......Page 543
 F......Page 544
 L......Page 545
 Q......Page 546
 V......Page 547
 Z......Page 548