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E-raamat: Bob Miller's High School Calc for the Clueless - Honors and AP Calculus AB & BC

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With Bob Miller at your side, you never have to be clueless about math again!

Algebra and calculus are tough on high school students like you. Professor Bob Miller, with more than 30 years' teaching experience, is a master at making the complex simple, and his now-classic series of Clueless study aids has helped tens of thousands understand the tough subjects.

Calculus-with its integrals and derivatives-is famous for tripping up even the quickest minds. Now Bob Miller-with his 30-plus years' experience teaching it-presents high school calculus in a clear, humorous, and engaging way.
Acknowledgments xi
To the Student xiii
The Beginning---Limits
1(22)
Informal Definition
1(6)
Limits as x Goes to Infinity
7(2)
Problems Involving lim x →0 sin x/x
9(2)
Formal Definition
11(5)
Limits as x Goes to Infinity, Formally
16(2)
Theorems on Limits
18(2)
Continuity
20(3)
The Basics
23(50)
Derivatives---Definition and Rules
23(20)
Implicit Differentiation
43(11)
Notations
47(7)
Antiderivatives and Definite Integrals
54(19)
Finding the Area under the Curve by Using the Definition of the Definite Integral
66(7)
Curve Sketching Made Easy
73(30)
Terms and Special Notations
73(1)
Intercepts
74(2)
Vertical Asymptotes
76(1)
Horizontal Asymptote Type 1
76(1)
Horizontal Asymptote Type 2
77(1)
Oblique (Slanted Line) Asymptote
77(1)
Curve Sketching by the Pieces
78(10)
Testing for Round Maximums and Minimums
88(11)
Other Aids
99(4)
Word Problems Made Easy . . . Well, Less Difficult
103(20)
Max, Min
104(10)
Related Rates
114(5)
The Gravity of the Situation
119(4)
Integral Applications
123(18)
Areas
123(7)
Volumes of Rotations
130(7)
Volumes by Section
137(4)
Odds and Ends
141(16)
Differentials
141(2)
Mean Value Theorem
143(5)
Approximations, Approximations
148(9)
Newton's Method
148(2)
Trapezoidal Method
150(1)
Parabolic Method
151(2)
Work, Work, Work
153(4)
Logarithms
157(4)
The Basic Laws of Logs
157(4)
Derivatives of ex, ax, Logs, Trig Functions, etc.
161(6)
Shorter Integrals
167(10)
Trig Integrals
169(2)
Exponential Integrals
171(2)
Inverse Trig Functions
173(4)
Exponential Growth and Decay
177(6)
What You Should Know From Before to Do the Next
183(4)
Longer Interorals
187(18)
Integration by Parts
187(9)
Partial Fractions
196(5)
Additional and Substitutions
201(3)
Area of a Circle
204(1)
Second Odds and Ends
205(14)
L'Hopital's Rule
205(4)
Improper Integrals
209(5)
Slope Fields
214(5)
Infinite Sequences
219(26)
Infinite Series, Including Which Test to Use (Very Important!)
222(14)
Which Test to Use
235(1)
A Preview of Power Series---Taylor's Theorem
236(9)
Taylor's Theorem
236(9)
Index 245


Bob Miller (East Brunswick, NJ) has been a lecturer in Mathematics at City College of New York, a branch of the City University of New York, for more than twenty-eight years.
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