9780071453172

Bob Miller's Calc for the Clueless: Precalc

by
  • ISBN13:

    9780071453172

  • ISBN10:

    0071453172

  • Edition: 3rd
  • Format: Paperback
  • Copyright: 2005-07-01
  • Publisher: McGraw-Hill Education
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Summary

Bob Miller's PreCalc for the Clueless, Third Edition,is jam-packed with tips, techniques, and surefire strategies to help students understand and advance in this challenging subject. In this third edition, new features include: Recent changes in the precalculus pedagogy implemented over the past seven years New sections explaining the fundamentals of algebra and trigonometry A new chapter on induction All the math needed for the new SAT Sample problems for every technique and topic

Author Biography

Bob Miller was a lecturer in mathematics at City College of New York for more than 30 years. His principal goal is to make the study of mathematics both easier and enjoyable for students.

Table of Contents

Acknowledgments ix
To the Student x
Lines, the Straight Kind
1(8)
Standard Form
1(8)
Quadratic Equations
9(6)
Solving a Quadratic (or Higher) by Factoring
9(2)
The Quadratic Formula
11(4)
Inequalities, Linear and Quadratic
15(8)
Linear Inequalities
15(1)
Quadratic Inequalities
16(7)
Absolute Value
23(4)
Exponents---Negative, Fractional
27(6)
Geometric Formulas and Facts You Must Know
33(4)
Squares, Rectangles, Boxes, and Cubes
33(1)
Circles
34(1)
Other Shapes
34(3)
Distances, Midpoints, Circles, and Parabolas
37(4)
Distances
37(1)
Midpoints
37(1)
Circles
38(1)
Parabolas
38(3)
Functions
41(16)
Functional Notation
42(9)
Finding the Ranges and Domains and Sketches of Functions (Beginning)
46(5)
Composite Functions
51(2)
Inverse Functions
53(4)
Linear Systems and More About y = x2
57(14)
Equations in Twos and Threes
57(1)
Two Equations in Two Unknowns
57(6)
Graphing
57(1)
Algebra: Substitution
58(2)
Algebra: Elimination
60(2)
Relating the Graph to the Algebra
62(1)
Three Equations in Three Unknowns
63(4)
Graphing a Point in 3D
64(1)
What Would It Look Like?
65(2)
y = x2, y = x3, and a Little More
67(4)
Trigonometry
71(38)
Angles
71(2)
Basic Definitions
73(1)
Multiples of 30°, 45°, 60°, and 90°
74(3)
Curve Sketching
77(6)
Identities
83(4)
Attacking Identities
85(2)
Trig Equations
87(5)
Domains and Ranges of the Trig Functions
92(1)
Double Angles, Half Angles, Sum and Difference of Two Angles
92(8)
Inverse Trig Functions
100(4)
Right-Angle Trig
103(1)
The Law of Sines
104(3)
Two Angles and a Side
105(1)
Two Sides and an Angle Opposite One of Those Sides
105(2)
The Law of Cosines
107(2)
Curve Sketching
109(14)
Polynomials
109(4)
Rational Functions
113(10)
Vertical Asymptotes
114(1)
Horizontal Asymptotes
115(8)
Modern Logarithms
123(8)
Parabolas II, Ellipses, and Hyperbolas
131(22)
Systems of Nonlinear Equations
144(9)
Writing Functions of x, the Algebraic Part of Calculus Word Problems
153(12)
The Binomial Theorem
165(4)
The Theory of Equations
169(8)
Theorem 1: The Fundamental Theorem of Algebra
170(1)
Theorem 2: Number of Roots
170(1)
Theorem 3: The Remainder Theorem
170(1)
Theorem 4: The Factor Theorem
170(1)
Theorem 5: The Rational Root Theorem
171(1)
Theorem 6: The Upper and Lower Bounds for Roots Theorem
172(1)
Theorem 7: Descartes' Rule of Signs
173(2)
What to Do If Nothing Else Works
175(2)
Finite Induction
177(4)
Progressions
181(10)
Arithmetic Progressions
181(4)
Finite Geometric Progressions
185(2)
Infinite Geometric Progressions
187(4)
Limits
191(8)
Finite Limits
191(5)
Limits Going to Infinity
196(3)
APPENDIX Synthetic Division and Sets
199(4)
Synthetic Division
199(1)
Sets
200(3)
Index 203(3)
About Bob Miller . . . In His Own Words 206

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