An edition of Barron's AP calculus
(2010)
Barron's AP calculus
10th ed.
by Shirley O. Hockett
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Overview: Both Calculus AB and Calculus BC are covered in this comprehensive AP test preparation manual. Prospective test takers will find four practice exams in Calculus AB and four more in Calculus BC, with all questions answered and solutions explained. The manual also provides a detailed 10-chapter review covering topics for both exams. The authors also offer an overview of the AP Calculus exams, which includes advice to students on making best use of their graphing calculators.
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Previews available in: English
| Edition | Availability |
|---|---|
1
Barron's AP calculus
2010, Barron's, Barron's Educational Series
in English
- 10th ed.
0764196758 9780764196751
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Book Details
Table of Contents
Introduction
Courses
Topics that may be tested on the calculus AB exam
Topics that may be tested on the calculus BC exam
Examinations
Graphing calculator: using your graphing calculator on the AP exam
Grading the examinations
CLEP calculus examination
This review book
Diagnostic Tests
Calculus AB
Calculus BC
Topical Review And Practice
Functions
Definitions
Special functions
Polynomial and other rational functions
Trigonometric functions
Exponential and logarithmic functions
Parametrically defined functions
Practice exercises
Limits And Continuity
Definitions and examples
Asymptotes
Theorems on limits
Limit of a quotient of polynomials
Other basic limits
Continuity
Practice exercises
Differentiation
Definition of derivative
Formulas
Chain rule; the derivative of a composite function
Differentiability and continuity
Estimating a derivative
Numerically
Graphically
Derivatives of parametrically
Defined functions
Implicit differentiation
Derivative of the inverse of a function
Mean value theorem
Indeterminate forms and L'Hopitals' rule
Recognizing a given limit as a derivative
Practice exercises
Applications of differential calculus
Slope; critical points
Tangents and normals
Increasing and decreasing functions
Case 1: Functions with continuous derivatives
Case 2: Functions whose derivatives have discontinuities
Maximum, minimum, and inflection points: definitions
Maximum, minimum, and inflection points: curve sketching
Case 1: Functions that are everywhere differentiable
Case 2: Functions whose derivatives may not exist everywhere
Global maximum or minimum
Case 1: Differentiable functions
Case 2: Functions that are not everywhere differentiable
Further aids in sketching
Optimization: problems involving maxima and minima
Relating a function and its derivatives graphically
Motion along a line
Motion along a curve: velocity and acceleration vectors
Tangent-line approximations
Related rates
Slope of a polar curve
Practice exercises
Antidifferentiation
Antiderivatives
Basic formulas
Integration by partial fractions
Integration by parts
Applications of antiderivates; differential equations
Practice exercises
Definite Integrals
Fundamental theorem of calculus (FTC); definition of definite integral
Properties of definite integrals
Integrals involving parametrically defined functions
Definition of definite integral as the limit of a sum: the fundamental theorem again
Approximations of the definite integral: Riemann sums
Using rectangles
Using trapezoids
Comparing approximating sums
Graphing a function from its derivative; another look
Interpreting 1n x as area
Average value
Practice exercises
Applications Of Integration To Geometry
Area
Area between curves
Using symmetry
Volume
Solids with known cross sections
Solids of revolution
Arc length
Improper integrals
Practice exercises
Further Applications Of Integration
Motion along a straight line
Motion along a plane curve
Other applications of Riemann sums
FTC: definite integral of a rate is net change
Practice exercises
Differential Equations
Basic definitions
Slope fields
Euler's method
Solving first-order differential
Equations analytically
Exponential growth and decay
Case 1: Exponential growth: dy_dt=ky
Case 2: Restricted growth: dy_dt=k(A-y)
Case 3: Logistic growth: dy_dt=ky(A-y)
Practice exercises
Sequences And Series
Sequences of real numbers
Infinite series
Definitions
Theorems about convergence or divergence of infinite series
Test for convergence of infinite series
Tests for convergence of nonnegative series
Alternating series and absolute convergence
Power series
Definition; convergence
Functions defined by power series
Finding a power series for a function: Taylor and Maclaurin series
Approximating functions with Taylor and Maclaurin polynomials
Taylor's formula with remainder; Lagrange error bound
Computations with power series
Power series over complex numbers
Practice exercises
Miscellaneous Multiple-Choice Practice Questions
Miscellaneous Free-Response Practice Exercises
AB Practice Examinations
AB one
AB two
AB three
BC Practice Examinations
BC one
BC two
BC three
Appendix: Formulas and theorems for reference
Index.
Edition Notes
Includes index.
System requirements for CD-ROM: PC with Windows Intel Pentium II 450 MHz or faster processor, 128 MB of RAM, 1024 x 768 display resolution, Windows 2000, XP, Vista, CD-ROM player ; Macintosh with PowerPC G3 500 MHz or faster, 128 MB of RAM, 1024 x 768 display resolution, Mac OS X v.10.1 through 10.4, CD-ROM player.
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