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3 | (5) |
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3 | (1) |
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4 | (1) |
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Prerequisites to AP Calculus |
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4 | (1) |
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The AP Calculus AB and BC Courses |
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4 | (1) |
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The AP Calculus Examinations |
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5 | (1) |
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Factors Leading to Success in AP Calculus |
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6 | (2) |
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Functions and Their Properties |
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8 | (31) |
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A Review of Basic Functions |
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8 | (12) |
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20 | (2) |
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22 | (6) |
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28 | (3) |
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Translations and Reflections |
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31 | (1) |
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32 | (7) |
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35 | (4) |
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39 | (19) |
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39 | (4) |
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Evaluating Limits as x Approaches a Finite Number c |
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43 | (3) |
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Evaluating Limits as x Approaches ±∞ |
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46 | (2) |
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Special Limits: lim sin/x and lim 1 -- cos x/x |
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48 | (2) |
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Evaluating Limits of a Piecewise-Defined Function |
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50 | (2) |
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52 | (6) |
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54 | (4) |
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58 | (40) |
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The Derivative of a Function |
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58 | (5) |
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The Average Rate of Change of a Function on an Interval |
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63 | (3) |
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The Definition of the Derivative |
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66 | (1) |
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67 | (6) |
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Recognizing the Form of the Derivative |
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73 | (5) |
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The Equation of a Tangent Line |
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78 | (3) |
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Differentiability vs. Continuity |
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81 | (1) |
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82 | (4) |
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Motion of a Freely Falling Object |
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86 | (2) |
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88 | (3) |
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91 | (2) |
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Derivatives of Parametric Equations |
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93 | (5) |
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94 | (4) |
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Applications of the Derivative |
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98 | (27) |
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Three Theorems: The Extreme Value Theorem, Rolle's Theorem, and the Mean Value Theorem |
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98 | (4) |
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102 | (8) |
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Concavity and the Second Derivative |
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110 | (3) |
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Curve Sketching and the Graphing Calculator |
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113 | (5) |
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118 | (7) |
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121 | (4) |
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Techniques and Applications of Antidifferentiation |
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125 | (55) |
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125 | (6) |
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Area Under a Curve: Approximation by Riemann Sums |
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131 | (7) |
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The Fundamental Theorem of Calculus |
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138 | (8) |
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The Accumulation Function: An Application of Part Two of the Fundamental Theorem |
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146 | (4) |
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Integration by the Change of Variable or u-Substitution Method |
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150 | (5) |
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Applications of the Integral: Average Value of a Function |
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155 | (2) |
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157 | (11) |
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168 | (4) |
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Arc Length and Area of a Surface of Revolution |
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172 | (8) |
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176 | (4) |
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Separable Differential Equations and Slope Fields |
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180 | (19) |
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Separable Differential Equations |
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180 | (5) |
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185 | (3) |
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The Connection Between a Slope Field and Its Differential Equation |
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188 | (11) |
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192 | (7) |
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199 | (14) |
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199 | (3) |
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Integration by the Method of Partial Fractions |
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202 | (4) |
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206 | (7) |
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209 | (4) |
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Polynomial Approximations and Infinite Series |
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213 | (40) |
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213 | (2) |
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215 | (2) |
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Derivation of the Taylor Polynomial Formula |
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217 | (4) |
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Finding New Polynomials from Old |
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221 | (4) |
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Error Formula for Taylor Polynomial Approximation |
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225 | (2) |
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227 | (15) |
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242 | (11) |
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248 | (5) |
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Logistic Growth, Euler's Method, and Other BC Topics |
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253 | (28) |
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The Logistic Growth Model |
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253 | (4) |
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Euler's Approximation Method |
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257 | (4) |
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Logarithmic Differentiation |
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261 | (2) |
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263 | (3) |
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266 | (15) |
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277 | (4) |
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281 | (40) |
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283 | (10) |
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293 | (9) |
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302 | (9) |
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311 | (10) |
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321 | (50) |
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323 | (8) |
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331 | (4) |
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335 | (11) |
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346 | (4) |
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350 | (6) |
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356 | (4) |
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360 | (1) |
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361 | (6) |
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367 | (4) |
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371 | (24) |
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371 | (7) |
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378 | (5) |
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383 | (6) |
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389 | (6) |
| Index |
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395 | |
Other versions by this Author