| How to Use This Book |
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ix | |
| Barron's Essential 5 |
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| Introduction |
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1 | (16) |
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1 | (1) |
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Topic Outline for the AB and BC Calculus Exams |
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1 | (6) |
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7 | (1) |
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The Graphing Calculator: Using Your Graphing Calculator on the AP Exam |
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8 | (4) |
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12 | (5) |
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Diagnostic Test Calculus AB |
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17 | (24) |
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Diagnostic Test Calculus BC |
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41 | (22) |
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TOPICAL REVIEW AND PRACTICE |
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63 | (26) |
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63 | (3) |
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66 | (3) |
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C Polynomial and Other Rational Functions |
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69 | (1) |
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D Trigonometric Functions |
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69 | (3) |
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E Exponential and Logarithmic Functions |
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72 | (1) |
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F Parametrically Defined Functions |
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73 | (3) |
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76 | (3) |
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79 | (10) |
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89 | (24) |
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A Definitions and Examples |
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89 | (5) |
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94 | (2) |
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96 | (2) |
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D Limit of a Quotient of Polynomials |
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98 | (1) |
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99 | (1) |
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99 | (6) |
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105 | (8) |
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113 | (46) |
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A Definition of Derivative |
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113 | (2) |
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115 | (1) |
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C The Chain Rule: The Derivative of a Composite Function |
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116 | (5) |
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D Differentiability and Continuity |
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121 | (1) |
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E Estimating a Derivative |
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122 | (4) |
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122 | (3) |
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125 | (1) |
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F Derivatives of Parametrically Defined Functions |
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126 | (2) |
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G Implicit Differentiation |
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128 | (2) |
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H Derivative of the Inverse of a Function |
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130 | (1) |
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131 | (2) |
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J Indeterminate Forms and L'Hospital's Rule |
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133 | (3) |
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K Recognizing a Given Limit as a Derivative |
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136 | (3) |
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139 | (20) |
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4 Applications of Differential Calculus |
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159 | (54) |
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159 | (2) |
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161 | (2) |
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C Increasing and Decreasing Functions |
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163 | (1) |
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Case I Functions with Continuous Derivatives |
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163 | (1) |
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Case II Functions Whose Derivatives Have Discontinuities |
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163 | (1) |
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D Maximum, Minimum, Concavity, and Inflection Points: Definitions |
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164 | (1) |
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E Maximum, Minimum, and Inflection Points: Curve Sketching |
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165 | (6) |
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Case I Functions That Are Everywhere Differentiable |
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165 | (4) |
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Case II Functions Whose Derivatives May Not Exist Everywhere |
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169 | (2) |
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F Global Maximum or Minimum |
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171 | (1) |
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Case I Differentiable Functions |
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171 | (1) |
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Case II Functions That Are Not Everywhere Differentiable |
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171 | (1) |
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G Further Aids in Sketching |
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171 | (2) |
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H Optimization: Problems Involving Maxima and Minima |
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173 | (4) |
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I Relating a Function and Its Derivatives Graphically |
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177 | (3) |
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180 | (2) |
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K Motion Along a Curve: Velocity and Acceleration Vectors |
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182 | (4) |
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L Tangent-Line Approximations |
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186 | (2) |
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188 | (2) |
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190 | (3) |
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193 | (20) |
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213 | (28) |
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213 | (1) |
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213 | (7) |
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C Integration by Partial Fractions |
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220 | (1) |
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221 | (3) |
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E Applications of Antiderivatives; Differential Equations |
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224 | (3) |
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227 | (14) |
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241 | (42) |
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A Fundamental Theorem of Calculus (FTC); Evaluation of Definite Integrals |
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241 | (1) |
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B Properties of Definite Integrals |
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241 | (5) |
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C Definition of Definite Integral as the Limit of a Riemann Sum |
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246 | (1) |
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D The Fundamental Theorem Again |
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247 | (1) |
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E Approximations of the Definite Integral; Riemann Sums |
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248 | (5) |
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248 | (2) |
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250 | (2) |
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E3 Comparing Approximating Sums |
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252 | (1) |
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F Graphing a Function from Its Derivative; Another Look |
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253 | (7) |
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G Interpreting In x as an Area |
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260 | (1) |
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261 | (9) |
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270 | (13) |
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7 Applications of Integration to Geometry |
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283 | (54) |
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283 | (7) |
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285 | (1) |
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286 | (2) |
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A3 Region Bounded by Polar Curve |
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288 | (2) |
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290 | (7) |
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B1 Solids with Known Cross Sections |
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290 | (2) |
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292 | (5) |
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C Length of Curve (Arc Length) |
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297 | (2) |
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299 | (10) |
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309 | (28) |
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8 Further Applications of Integration |
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337 | (20) |
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A Motion Along a Straight Line |
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337 | (2) |
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B Motion Along a Plane Curve |
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339 | (3) |
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C Other Applications of Riemann Sums |
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342 | (2) |
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D FTC: Definite Integral of a Rate Is Net Change |
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344 | (2) |
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346 | (11) |
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357 | (42) |
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357 | (1) |
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358 | (5) |
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363 | (4) |
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D Solving First-Order Differential Equations Analytically |
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367 | (2) |
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E Exponential Growth and Decay |
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369 | (12) |
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Case I Exponential Growth |
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369 | (4) |
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Case II Restricted Growth |
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373 | (3) |
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376 | (5) |
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381 | (18) |
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399 | (44) |
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A Sequences of Real Numbers |
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399 | (1) |
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400 | (11) |
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400 | (2) |
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B2 Theorems About Convergence or Divergence of Infinite Series |
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402 | (1) |
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B3 Tests for Convergence of Infinite Series |
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403 | (1) |
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B4 Tests for Convergence of Nonnegative Series |
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404 | (4) |
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B5 Alternating Series and Absolute Convergence |
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408 | (3) |
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411 | (20) |
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C1 Definitions; Convergence |
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411 | (2) |
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C2 Functions Defined by Power Series |
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413 | (2) |
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C3 Finding a Power Series for a Function: Taylor and Maclaurin Series |
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415 | (3) |
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C4 Approximating Functions with Taylor and Maclaurin Polynomials |
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418 | (5) |
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C5 Taylor's Formula with Remainder; Lagrange Error Bound |
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423 | (2) |
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C6 Computations with Power Series |
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425 | (4) |
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C7 Power Series over Complex Numbers |
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429 | (2) |
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431 | (12) |
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11 Miscellaneous Multiple-Choice Practice Questions |
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443 | (32) |
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12 Miscellaneous Free-Response Practice Exercises |
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475 | (30) |
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505 | (24) |
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529 | (26) |
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555 | (28) |
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583 | (22) |
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605 | (20) |
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625 | (20) |
| Appendix: Formulas and Theorems for Reference |
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645 | (8) |
| Index |
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