| Barron's Essential 5 |
|
vi | |
| Introduction |
|
1 | (20) |
|
|
|
1 | (1) |
|
Topic Outline for the AB and BC Calculus Exams |
|
|
1 | (7) |
|
|
|
8 | (1) |
|
The Graphing Calculator: Using Your Graphing Calculator on the AP Exam |
|
|
8 | (5) |
|
|
|
13 | (1) |
|
|
|
14 | (1) |
|
|
|
15 | (6) |
|
|
|
|
|
|
21 | (26) |
|
|
|
47 | (22) |
|
TOPICAL REVIEW AND PRACTICE |
|
|
|
|
|
69 | (24) |
|
|
|
69 | (3) |
|
|
|
72 | (3) |
|
C Polynomial and Other Rational Functions |
|
|
75 | (1) |
|
D Trigonometric Functions |
|
|
75 | (3) |
|
E Exponential and Logarithmic Functions |
|
|
78 | (1) |
|
F Parametrically Defined Functions |
|
|
79 | (3) |
|
|
|
82 | (3) |
|
|
|
85 | (8) |
|
|
|
93 | (24) |
|
A Definitions and Examples |
|
|
93 | (5) |
|
|
|
98 | (1) |
|
|
|
99 | (2) |
|
D Limit of a Quotient of Polynomials |
|
|
101 | (1) |
|
|
|
102 | (1) |
|
|
|
103 | (5) |
|
|
|
108 | (9) |
|
|
|
117 | (46) |
|
A Definition of Derivative |
|
|
117 | (2) |
|
|
|
119 | (1) |
|
C The Chain Rule; the Derivative of a Composite Function |
|
|
120 | (5) |
|
D Differentiability and Continuity |
|
|
125 | (3) |
|
E Estimating a Derivative |
|
|
126 | (1) |
|
|
|
126 | (2) |
|
|
|
128 | (1) |
|
F Derivatives of Parametrically Defined Functions |
|
|
129 | (2) |
|
G Implicit Differentiation |
|
|
131 | (2) |
|
H Derivative of the Inverse of a Function |
|
|
133 | (1) |
|
|
|
134 | (2) |
|
J Indeterminate Forms and L'Hospital's Rule |
|
|
136 | (3) |
|
K Recognizing a Given Limit as a Derivative |
|
|
139 | (2) |
|
|
|
141 | (22) |
|
4 Applications of Differential Calculus |
|
|
163 | (54) |
|
|
|
163 | (2) |
|
|
|
165 | (1) |
|
C Increasing and Decreasing Functions |
|
|
166 | (1) |
|
Case I Functions with Continuous Derivatives |
|
|
166 | (1) |
|
Case II Functions Whose Derivatives Have Discontinuities |
|
|
167 | (1) |
|
D Maximum, Minimum, Concavity, and Inflection Points: Definitions |
|
|
167 | (1) |
|
E Maximum, Minimum, and Inflection Points: Curve Sketching |
|
|
168 | (6) |
|
Case I Functions That Are Everywhere Differentiable |
|
|
168 | (4) |
|
Case II Functions Whose Derivatives May Not Exist Everywhere |
|
|
172 | (2) |
|
F Global Maximum or Minimum |
|
|
174 | (1) |
|
Case I Differentiable Functions |
|
|
174 | (1) |
|
Case II Functions That Are Not Everywhere Differentiable |
|
|
174 | (1) |
|
G Further Aids in Sketching |
|
|
174 | (2) |
|
H Optimization: Problems Involving Maxima and Minima |
|
|
176 | (4) |
|
I Relating a Function and Its Derivatives Graphically |
|
|
180 | (3) |
|
|
|
183 | (2) |
|
K Motion Along a Curve: Velocity and Acceleration Vectors |
|
|
185 | (3) |
|
L Tangent-Line Approximations |
|
|
188 | (3) |
|
|
|
191 | (2) |
|
|
|
193 | (2) |
|
|
|
195 | (22) |
|
|
|
217 | (30) |
|
|
|
217 | (1) |
|
|
|
217 | (7) |
|
C Integration by Partial Fractions |
|
|
224 | (1) |
|
|
|
225 | (3) |
|
E Applications of Antiderivatives; Differential Equations |
|
|
228 | (3) |
|
|
|
231 | (16) |
|
|
|
247 | (40) |
|
A Fundamental Theorem of Calculus (FTC); Evaluation of Definite Integral |
|
|
247 | (1) |
|
B Properties of Definite Integrals |
|
|
247 | (5) |
|
C Definition of Definite Integral as the Limit of a Riemann Sum |
|
|
252 | (1) |
|
D The Fundamental Theorem Again |
|
|
253 | (1) |
|
E Approximations of the Definite Integral; Riemann Sums |
|
|
254 | (5) |
|
|
|
254 | (2) |
|
|
|
256 | (2) |
|
E3 Comparing Approximating Sums |
|
|
258 | (1) |
|
F Graphing a Function from Its Derivative; Another Look |
|
|
259 | (7) |
|
G Interpreting In x as an Area |
|
|
266 | (1) |
|
|
|
267 | (8) |
|
|
|
275 | (12) |
|
7 Applications of Integration to Geometry |
|
|
287 | (54) |
|
|
|
287 | (7) |
|
|
|
289 | (1) |
|
|
|
290 | (4) |
|
|
|
294 | (7) |
|
B1 Solids with Known Cross Sections |
|
|
294 | (2) |
|
|
|
296 | (5) |
|
C Length of Curve (Arc Length) |
|
|
301 | (2) |
|
|
|
303 | (10) |
|
|
|
313 | (28) |
|
8 Further Applications of Integration |
|
|
341 | (18) |
|
A Motion Along a Straight Line |
|
|
341 | (2) |
|
B Motion Along a Plane Curve |
|
|
343 | (3) |
|
C Other Applications of Riemann Sums |
|
|
346 | (2) |
|
D FTC: Definite Integral of a Rate Is Net Change |
|
|
348 | (11) |
|
|
|
350 | (9) |
|
|
|
359 | (40) |
|
|
|
359 | (1) |
|
|
|
360 | (5) |
|
|
|
365 | (4) |
|
D Solving First-Order Differential Equations Analytically |
|
|
369 | (2) |
|
E Exponential Growth and Decay |
|
|
371 | (12) |
|
Case I Exponential Growth |
|
|
371 | (4) |
|
Case II Restricted Growth |
|
|
375 | (3) |
|
|
|
378 | (5) |
|
|
|
383 | (16) |
|
|
|
399 | (42) |
|
A Sequences of Real Numbers |
|
|
399 | (1) |
|
|
|
400 | (10) |
|
|
|
400 | (2) |
|
B2 Theorems About Convergence or Divergence of Infinite Series |
|
|
402 | (1) |
|
B3 Tests for Convergence of Infinite Series |
|
|
403 | (1) |
|
B4 Tests for Convergence of Nonnegative Series |
|
|
404 | (3) |
|
B5 Alternating Series and Absolute Convergence |
|
|
407 | (3) |
|
|
|
410 | (18) |
|
C1 Definitions; Convergence |
|
|
410 | (2) |
|
C2 Functions Defined by Power Series |
|
|
412 | (2) |
|
C3 Finding a Power Series for a Function: Taylor and Maclaurin Series |
|
|
414 | (3) |
|
C4 Approximating Functions with Taylor and Maclaurin Polynomials |
|
|
417 | (4) |
|
C5 Taylor's Formula with Remainder; Lagrange Error Bound |
|
|
421 | (2) |
|
C6 Computations with Power Series |
|
|
423 | (4) |
|
C7 Power Series over Complex Numbers |
|
|
427 | (1) |
|
|
|
428 | (13) |
|
11 Miscellaneous Multiple-Choice Practice Questions |
|
|
441 | (32) |
|
12 Miscellaneous Free-Response Practice Exercises |
|
|
473 | (28) |
| AB PRACTICE EXAMINATIONS |
|
|
|
|
501 | (24) |
|
|
|
525 | (26) |
|
|
|
551 | (28) |
| BC PRACTICE EXAMINATIONS |
|
|
|
|
579 | (22) |
|
|
|
601 | (22) |
|
|
|
623 | (22) |
| Appendix: Formulas and Theorems for Reference |
|
645 | (8) |
| Index |
|
653 | |
