Bob Miller's Calc for the Clueless: Precalc

by Miller, Bob

• ISBN13: 9780071453172
• ISBN10: 0071453172
• Edition: 3rd
• Format: Paperback
• Copyright: 2005-07-01
• Publisher: McGraw Hill

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