Barron's AP Calculus
by Brock, David; Hockett, Shirley O.Edition: 11th
Format: Paperback
Pub. Date: 2012-02-01
Publisher(s): Barrons Test Prep
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Summary
Both Calculus AB and Calculus BC are covered in this comprehensive AP test preparation manual. Main features include: Four practice exams in Calculus AB and four more in Calculus BC All test questions answered with solutions explained A detailed subject review covering topics for both exams Advice to students on efficient use of their graphing calculators An enclosed CD-ROM presents two more practice tests with answers, one in Calculus AB, and the other in Calculus BC
Table of Contents
| Barron's Essential 5 | p. vii |
| Introduction | p. 1 |
| The Courses | p. 1 |
| Topics That May Be Tested on the Calculus AB Exam | p. 1 |
| Topics That May Be Tested on the Calculus BC Exam | p. 2 |
| The Examinations | p. 3 |
| The Graphing Calculator: Using Your Graphing Calculator on the AP Exam | p. 4 |
| Grading the Examinations | p. 9 |
| The CLEP Calculus Examination | p. 10 |
| This Review Book | p. 10 |
| Flash Cards | p. 11 |
| Diagnostic Tests | |
| Calculus AB | p. 17 |
| Calculus BC | p. 43 |
| Topical Review and Practice | |
| Functions | p. 67 |
| Definitions | p. 67 |
| Special Functions | p. 70 |
| Polynomial and Other Rational Functions | p. 73 |
| Trigonometric Functions | p. 73 |
| Exponential and Logarithmic Functions | p. 76 |
| Parametrically Defined Functions | p. 77 |
| Practice Exercises | p. 80 |
| Limits and Continuity | p. 87 |
| Definitions and Examples | p. 87 |
| Asymptotes | p. 92 |
| Theorems on Limits | p. 93 |
| Limit of a Quotient of Polynomials | p. 95 |
| Other Basic Limits | p. 96 |
| Continuity | p. 97 |
| Practice Exercises | p. 102 |
| Differentiation | p. 111 |
| Definition of Derivative | p. 111 |
| Formulas | p. 113 |
| The Chain Rule; the Derivative of a Composite Function | p. 114 |
| Differentiability and Continuity | p. 118 |
| Estimating a Derivative | p. 119 |
| Numerically | p. 119 |
| Graphically | p. 122 |
| Derivatives of Parametrically Defined Functions | p. 123 |
| Implicit Differentiation | p. 124 |
| Derivative of the Inverse of a Function | p. 126 |
| The Mean Value Theorem | p. 128 |
| Indeterminate Forms and L'Hôpital's Rule | p. 129 |
| Recognizing a Given Limit as a Derivative | p. 132 |
| Practice Exercises | p. 134 |
| Applications of Differential Calculus | p. 159 |
| Slope; Critical Points | p. 159 |
| Tangents and Normals | p. 161 |
| Increasing and Decreasing Functions | p. 162 |
| Functions with Continuous Derivatives | p. 162 |
| Functions Whose Derivatives Have Discontinuities | p. 163 |
| Maximum, Minimum, and Inflection Points: Definitions | p. 163 |
| Maximum, Minimum, and Inflection Points: Curve Sketching | p. 164 |
| Functions That Are Everywhere Differentiable | p. 164 |
| Functions Whose Derivatives May Not Exist Everywhere | p. 168 |
| Global Maximum or Minimum | p. 169 |
| Differentiable Functions | p. 169 |
| Functions That Are Not Everywhere Differentiable | p. 170 |
| Further Aids in Sketching | p. 170 |
| Optimization: Problems Involving Maxima and Minima | p. 172 |
| Relating a Function and Its Derivatives Graphically | p. 176 |
| Motion Along a Line | p. 179 |
| Motion Along a Curve: Velocity and Acceleration Vectors | p. 181 |
| Tangent-Line Approximations | p. 185 |
| Related Rates | p. 188 |
| Slope of a Polar Curve | p. 190 |
| Practice Exercises | p. 192 |
| Antidifferentiation | p. 215 |
| Antiderivatives | p. 215 |
| Basic Formulas | p. 215 |
| Integration by Partial Fractions | p. 223 |
| Integration by Parts | p. 224 |
| Applications of Antiderivatives; Differential Equations | p. 227 |
| Practice Exercises | p. 229 |
| Definite Integrals | p. 249 |
| Fundamental Theorem of Calculus (FTC); Definition of Definite Integral | p. 249 |
| Properties of Definite Integrals | p. 249 |
| Integrals Involving Parametrically Defined Functions | p. 254 |
| Definition of Definite Integral as the Limit of a Sum: The Fundamental Theorem Again | p. 255 |
| Approximations of the Definite | |
| Integral; Riemann Sums | p. 257 |
| Using Rectangles | p. 257 |
| Using Trapezoids | p. 258 |
| Comparing Approximating Sums | p. 260 |
| Graphing a Function from Its | |
| Derivative; Another Look | p. 262 |
| Interpreting In x as an Area | p. 269 |
| Average Value | p. 270 |
| Practice Exercises | p. 277 |
| Applications of Integration to Geometry | p. 291 |
| Area | p. 291 |
| Area Between Curves | p. 293 |
| Using Symmetry | p. 293 |
| Volume | p. 298 |
| Solids with Known Cross Sections | p. 298 |
| Solids of Revolution | p. 300 |
| Arc Length | p. 305 |
| Improper Integrals | p. 307 |
| Practice Exercises | p. 317 |
| Further Applications of Integration | p. 345 |
| Motion Along a Straight Line | p. 345 |
| Motion Along a Plane Curve | p. 347 |
| Other Applications of Riemann Sums | p. 350 |
| FTC: Definite Integral of a Rate Is Net Change | p. 352 |
| Practice Exercises | p. 356 |
| Differential Equations | p. 367 |
| Basic Definitions | p. 367 |
| Slope Fields | p. 369 |
| Euler's Method | p. 373 |
| Solving First-Order Differential Equations Analytically | p. 377 |
| Exponential Growth and Decay | p. 379 |
| Exponential Growth | p. 379 |
| Restricted Growth | p. 383 |
| Logistic Growth | p. 386 |
| Practice Exercises | p. 391 |
| Sequences and Series | p. 409 |
| Sequences of Real Numbers | p. 409 |
| Infinite Series | p. 410 |
| Definitions | p. 410 |
| Theorems About Convergence or Divergence of Infinite Series | p. 412 |
| Tests for Convergence of Infinite Series | p. 413 |
| Tests for Convergence of Nonnegative Series | p. 414 |
| Alternating Series and Absolute Convergence | p. 418 |
| Power Series | p. 421 |
| Definitions; Convergence | p. 421 |
| Functions Defined by Power Series | p. 423 |
| Finding a Power Series for a Function: Taylor and Maclaurin Series | p. 425 |
| Approximating Functions with Taylor and Maclaurin Polynomials | p. 429 |
| Taylor's Formula with Remainder; Lagrange Error Bound | p. 433 |
| Computations with Power Series | p. 436 |
| Power Series over Complex Numbers | p. 439 |
| Practice Exercises | p. 440 |
| Miscellaneous Multiple-Choice Practice Questions | p. 455 |
| Miscellaneous Free-Response Practice Exercises | p. 491 |
| Practice Examinations | |
| One | p. 519 |
| Two | p. 545 |
| Three | p. 573 |
| Practice Examinations | |
| One | p. 603 |
| Two | p. 625 |
| Three | p. 649 |
| Appendix: Formulas and Theorems for Reference | p. 673 |
| Index | p. 683 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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