Introduction | p. xi |
Limits | p. 1 |
What Is a Limit? | p. 1 |
Limits of Trigonometric Functions | p. 6 |
Practice Problem Set 1 | p. 10 |
Continuity | p. 13 |
The Definition of Continuity | p. 14 |
Types of Discontinuities | p. 16 |
Practice Problem Set 2 | p. 21 |
The Definition of the Derivative | p. 23 |
Deriving the Formula | p. 23 |
The Slope of a Curve | p. 25 |
The Secant and the Tangent | p. 25 |
Differentiability | p. 28 |
Practice Problem Set 3 | p. 31 |
Basic Differentiation | p. 33 |
Notation | p. 33 |
The Power Rule | p. 34 |
The Addition Rule | p. 36 |
Higher Order Derivatives | p. 37 |
Practice Problem Set 4 | p. 38 |
The Product Rule | p. 39 |
The Quotient Rule | p. 41 |
The Chain Rule | p. 42 |
Practice Problem Set 5 | p. 47 |
Derivatives of Trig Functions | p. 48 |
Practice Problem Set 6 | p. 52 |
Implicit Differentiation | p. 55 |
How to Do It | p. 55 |
Second Derivatives | p. 61 |
Practice Problem Set 7 | p. 65 |
Basic Applications of the Derivative | p. 67 |
Equations of Tangent Lines and Normal Lines | p. 67 |
Practice Problem Set 8 | p. 73 |
The Mean Value Theorem for Derivatives | p. 74 |
Rolle's Theorem | p. 76 |
Practice Problem Set 9 | p. 78 |
Maxima and Minima | p. 79 |
Applied Maxima and Minima Problems | p. 79 |
Practice Problem Set 10 | p. 90 |
Curve Sketching | p. 91 |
Practice Problem Set 11 | p. 104 |
Motion | p. 105 |
Related Rates | p. 105 |
Practice Problem Set 12 | p. 110 |
Position, Velocity, and Acceleration | p. 111 |
Practice Problem Set 13 | p. 115 |
Exponential and Logarithmic Functions, Part One | p. 117 |
The Derivative of In x | p. 118 |
The Derivative of e[superscript x] | p. 119 |
The Derivative of log[subscript a]x | p. 119 |
The Derivative of a[superscript x] | p. 120 |
Practice Problem Set 14 | p. 124 |
Other Topics in Differential Calculus | p. 125 |
The Derivative of an Inverse Function | p. 125 |
Practice Problem Set 15 | p. 128 |
Derivatives of Parametric Functions | p. 129 |
Practice Problem Set 16 | p. 133 |
L'Hopital's Rule | p. 134 |
Practice Problem Set 17 | p. 138 |
Differentials | p. 138 |
Practice Problem Set 18 | p. 141 |
Logarithmic Differentiation | p. 142 |
Practice Problem Set 19 | p. 147 |
The Integral | p. 149 |
The Antiderivative | p. 149 |
Integrals of Trig Functions | p. 151 |
Addition and Subtraction | p. 152 |
Practice Problem Set 20 | p. 156 |
U-Substitution | p. 157 |
Practice Problem Set 21 | p. 162 |
Definite Integrals | p. 163 |
Area Under a Curve | p. 163 |
The Fundamental Theorem of Calculus | p. 170 |
The Trapezoid Rule | p. 171 |
Practice Problem Set 22 | p. 177 |
The Mean Value Theorem for Integrals | p. 177 |
The Second Fundamental Theorem of Calculus | p. 179 |
Practice Problem Set 23 | p. 181 |
Exponential and Logarithmic Functions, Part Two | p. 183 |
More Integrals of Trig Functions | p. 184 |
Integrating e[superscript x] and a[superscript x] | p. 186 |
Practice Problem Set 24 | p. 190 |
The Area Between Two Curves | p. 191 |
Vertical Slices | p. 192 |
Horizontal Slices | p. 195 |
Practice Problem Set 25 | p. 200 |
The Volume of a Solid of Revolution | p. 201 |
Washers and Disks | p. 202 |
Cylindrical Shells | p. 207 |
Volumes of Solids with Known Cross-Sections | p. 211 |
Practice Problem Set 26 | p. 218 |
Integration By Parts | p. 219 |
The Formula | p. 219 |
Practice Problem Set 27 | p. 224 |
Trig Functions | p. 225 |
Inverse Trig Functions | p. 225 |
Practice Problem Set 28 | p. 231 |
Advanced Integrals of Trig Functions | p. 232 |
Practice Problem Set 29 | p. 238 |
Other Applications of the Integral | p. 239 |
Length of a Curve | p. 239 |
Parametric Functions | p. 241 |
Practice Problem Set 30 | p. 243 |
The Method of Partial Fractions | p. 244 |
Practice Problem Set 31 | p. 249 |
Improper Integrals | p. 250 |
Practice Problem Set 32 | p. 254 |
Calculus of Polar Curves | p. 255 |
Practice Problem Set 33 | p. 259 |
Differential Equations | p. 261 |
Separation of Variables | p. 261 |
Euler's Method | p. 266 |
Slope Fields | p. 272 |
Practice Problem Set 34 | p. 275 |
Infinite Series | p. 277 |
Sequences and Series | p. 277 |
Geometric Series | p. 279 |
The Ratio Test | p. 281 |
Alternating Series | p. 282 |
Integral Test | p. 283 |
Comparison Test | p. 284 |
Power Series | p. 285 |
Taylor Series and Polynomials | p. 286 |
Practice Problem Set 35 | p. 290 |
Answers to Practice Problem Sets | p. 291 |
The Princeton Review AP Calculus AB Practice Test 1 | p. 307 |
Answers and Explanations to AB Practice Test 1 | p. 331 |
The Princeton Review AP Calculus AB Practice Test 2 | p. 369 |
Answers and Explanations to AB Practice Test 2 | p. 395 |
The Princeton Review AP Calculus AB Practice Test 3 | p. 429 |
Answers and Explanations to AB Practice Test 3 | p. 459 |
The Princeton Review AP Calculus BC Practice Test 1 | p. 497 |
Answers and Explanations to BC Practice Test 1 | p. 523 |
The Princeton Review AP Calculus BC Practice Test 2 | p. 567 |
Answers and Explanations to BC Practice Test 2 | p. 599 |
Appendix | p. 639 |
Derivatives and Integrals That You Should Know | p. 640 |
Prerequisite Mathematics | p. 641 |
Table of Contents provided by Ingram. All Rights Reserved. |