Cengage Advantage Books: Precalculus A Problems-Oriented Approach

by Cohen, David

• ISBN13: 9780314069214
• ISBN10: 0314069216
• Edition: 5th
• Format: Hardcover
• Copyright: 1996-08-01
• Publisher: Brooks Cole

Summary

Precalculus: A Problems-Oriented Approach offers a fairly rigorous lead-in to calculus using the right triangle approach to trigonometry. A graphical perspective gives students a visual understanding of concepts. The text may be used with any graphing utility, or with none at all, with equal ease. Modeling provides students with real-world connections to the problems. The author is know for his clear writing style and numerous quality exercises and applications.

Table of Contents

Algebra Background for Precalculus	1	(34)
Sets of Real Numbers	1	(5)
Absolute Value	6	(5)
Polynomials and Factoring	11	(9)
Quadratic Equations	20	(15)
Coordinates, Graphs, and Inequalities	35	(66)
Rectangular Coordinates	35	(12)
Graphs and Equations, A Second Look	47	(10)
Equations of Lines	57	(12)
Symmetry and Graphs	69	(8)
Inequalities	77	(8)
More on Inequalities	85	(16)
Functions	101	(74)
The Definition of a Function	101	(12)
The Graph of a Function	113	(17)
Techniques in Graphing	130	(12)
Methods of Combining Functions. Iteration	142	(12)
Inverse Functions	154	(21)
Polynomial and Rational Functions. Applications to Iteration and Optimization	175	(95)
Linear Functions	175	(14)
Quadratic Functions	189	(9)
More on Iteration. Quadratics and Population Growth	198	(17)
Applied Functions: Setting up Equations	215	(12)
Maximum and Minimum Problems	227	(11)
Polynomial Functions	238	(13)
Rational Functions	251	(19)
Exponential and Logarithmic Functions	270	(87)
Exponential Functions	271	(9)
The Exponential Function y = ex	280	(9)
Logarithmic Functions	289	(12)
Properties of Logarithms	301	(9)
Equations and Inequalities with Logs and Exponents	310	(11)
Compound Interest	321	(11)
Exponential Growth and Decay	332	(25)
Trigonometric Functions of Angles	357	(51)
Trigonometric Functions of Acute Angles	357	(10)
Algebra and the Trigonometric Functions	367	(7)
Right-Triangle Applications	374	(9)
Trigonometric Functions of Angles	383	(12)
Trigonometric Identities	395	(13)
Trigonometric Functions of Real Numbers	408	(75)
Radian Measure	408	(9)
Radian Measure and Geometry	417	(10)
Trigonometric Functions of Real Numbers	427	(11)
Graphs of the Sine and the Cosine Functions	438	(16)
Graphs of y = A sin(Bx - C) and y = A cos(Bx - C)	454	(8)
Simple Harmonic Motion	462	(5)
Graphs of the Tangent and the Reciprocal Functions	467	(16)
Analytical Trigonometry	483	(55)
The Addition Formulas	483	(9)
The Double-Angle Formulas	492	(10)
The Product-to-Sum and Sum-to-Product Formulas	502	(5)
Trigonometric Equations	507	(11)
The Inverse Trigonometric Functions	518	(20)
Additional Topics in Trigonometry	538	(62)
The Law of Sines and the Law of Cosines	538	(15)
Vectors in the Plane, A Geometric Approach	553	(7)
Vectors in the Plane, An Algebraic Approach	560	(8)
Parametric Equations	568	(8)
Introduction to Polar Coordinates	576	(9)
Curves in Polar Coordinates	585	(15)
Systems of Equations	600	(72)
Systems of Two Linear Equations in Two Unknowns	600	(11)
Gaussian Elimination	611	(8)
Matrices	619	(12)
The Inverse of a Square Matrix	631	(7)
Determinants and Cramer's Rule	638	(13)
Nonlinear Systems of Equations	651	(7)
Systems of Inequalities	658	(14)
Analytic Geometry	672	(80)
The Basic Equations	672	(9)
The Parabola	681	(11)
Tangents to Parabolas (Optional)	692	(3)
The Ellipse	695	(15)
The Hyperbola	710	(11)
The Focus-Directrix Property of Conics	721	(9)
The Conics in Polar Coordinates	730	(6)
Rotation of Axes	736	(16)
Roots of Polynomial Equations	752	(70)
The Complex Number System	752	(8)
Division of Polynomials	760	(7)
Roots of Polynomial Equations: The Remainder Theorem and the Factor Theorem	767	(8)
The Fundamental Theorem of Algebra	775	(9)
Rational and Irrational Roots	784	(8)
Conjugate Roots and Descartes's Rule of Signs	792	(6)
Introduction to Partial Fractions	798	(7)
More About Partial Fractions	805	(17)
Additional Topics	822	(33)
Mathematical Induction	822	(6)
The Binomial Theorem	828	(10)
Introduction to Sequences and Series	838	(7)
Arithmetic Sequences and Series	845	(5)
Geometric Sequences and Series	850	(5)
DeMoivre's Theorem	855
APPENDIXES	A-1
A.1 Using a Graphing Utility	A-3
A.2 Significant Digits and Calculators	A-7
A.3 Properties of the Real Numbers	A-11
A.4 √2 Is Irrational	A-18
A.5 Review of Integer Exponents and n th Roots	A-19
A.6 Review of Rational Exponents	A-26
TABLES	A-29
1 Exponential Functions	A-30
2 Logarithms to the Base Ten	A-31
3 Natural Logarithms	A-33
4 Values of Trigonometric Functions	A-34
Answers to Selected Exercises	A-41
Index	I-1