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College Algebra (with CD-ROM, BCA/iLrn™ Tutorial, and InfoTrac),9780534405991

College Algebra (with CD-ROM, BCA/iLrn™ Tutorial, and InfoTrac)

by ; ;
Edition:
4th
ISBN13:

9780534405991

ISBN10:
0534405991
Format:
Hardcover
Pub. Date:
11/6/2003
Publisher(s):
Cengage Learning
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Summary

P. PREREQUISITES. Chapter Overview. Modeling the Real World. Real Numbers. Integer Exponents. Rational Exponents and Radicals. Algebraic Expressions. Discovery Project: Visualizing a Formula. Factoring Algebraic Expressions. Rational Expressions. Focus on Problem Solving: General Principles. 1. EQUATIONS AND INEQUALITIES. Chapter Overview. Equations. Modeling with Linear Equations. Discovery Project: Equations Through the Ages. Quadratic Equations. Complex Numbers. Other Types of Equations. Inequalities. Absolute Value Equations and Inequalities. Focus on Modeling: Making the Best Decisions. 2. COORDINATES AND GRAPHS. Chapter Overview. The Coordinate Plane. Discovery Project: Visualizing Data. Graphs of Equations in Two Variables. Graphing Calculators: Solving Equations Graphically. Lines. Modeling: Variation. Focus on Modeling: Fitting Lines to Data. 3. FUNCTIONS. Chapter Overview. What is a Function?. Graphs of Functions. Increasing and Decreasing Functions: Average Rate of Change. Transformations of Functions. Quadratic Functions; Maxima and Minima. Combining Functions. Discovery Project: Iteration and Chaos. One-to-One Functions and Their Inverses. Focus on Modeling: Modeling with Functions. 4. POLYNOMIAL AND RATIONAL FUNCTIONS. Chapter Overview. Polynomial Functions and Their Graphs. Dividing Polynomials. Real Zeros of Polynomials. Discovery Project: Zeroing in on a Zero. Complex Zeros and the Fundamental Theorem of Algebra. Rational Functions. Focus on Modeling: Fitting Polynomials to Data. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Chapter Overview. Exponential Functions. Discovery Project: Exponential Explosion. Logarithmic Functions. Laws of Logarithms. Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions. Focus on Modeling: Fitting Exponential and Power Curves to Data. 6. SYSTEMS OF EQUATIONS AND INEQUALITIES. Chapter Overview. Systems of Equations. Systems of Linear Equations in Two Variables. Systems of Linear Equations in Several Variables. Discovery Project: Exact Fit Versus Best Fit. Systems of Inequalities. Partial Fractions. Focus on Modeling: Linear Programming. 7. MATRICES AND DETERMINANTS. Chapter Overview. Matrix Representation of Linear Systems. The Algebra of Matrices. Discovery Project: Will the Specie Survive?. Inverses of Matrices and Matrix Equations. Determinants and Cramer's Rule. Focus on Modeling: Computer Graphics. 8. CONIC SECTIONS. Chapter Overview. Parabolas. Laboratory Project: Rolling Down a Ramp. Ellipses. Hyperbolas. Shifted Conics. Focus on Modeling: Conics in Architecture. 9. SEQUENCES AND SERIES. Chapter Overview. Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Discovery Project: Finding Patterns. Mathematics of Finance: Annuities. Mathematical Induction. The Binomial Theorem. Focus on Modeling: Modeling with Recursive Sequences. 10. COUNTING AND PROBABILITY. Chapter Overview. Counting Principles. Permutations and Combinations. Probability. Laboratory Project: Small Samples, Big Results. Binomial Probability. Expected Value. Focus on Modeling: The Monte Carlo Method.

Table of Contents

Preface xi
To the Student xvii
Calculators and Calculations xviii
P Prerequisites 2(70)
Chapter Overview
3(1)
P.1 Modeling the Real World
4(8)
P.2 Real Numbers
12(11)
P.3 Integer Exponents
23(8)
P.4 Rational Exponents and Radicals
31(6)
P.5 Algebraic Expressions
37(7)
DISCOVERY PROJECT Visualizing a Formula
43(1)
P.6 Factoring
44(6)
P.7 Rational Expressions
50(10)
Chapter P Review
60(3)
Chapter P Test
63(9)
FOCUS ON PROBLEM SOLVING General Principles
64(8)
1 Equations and Inequalities 72(76)
Chapter Overview
73(1)
1.1 Basic Equations
74(9)
1.2 Modeling with Equations
83(14)
DISCOVERY PROJECT Equations through the Ages
96(1)
1.3 Quadratic Equations
97(11)
1.4 Complex Numbers
108(7)
1.5 Other Types of Equations
115(9)
1.6 Inequalities
124(11)
1.7 Absolute Value Equations and Inequalities
135(3)
Chapter 1 Review
138(3)
Chapter 1 Test
141(7)
FOCUS ON MODELING Making the Best Decisions
142(6)
2 Coordinates and Graphs 148(64)
2.1 The Coordinate Plane
150(10)
DISCOVERY PROJECT Visualizing Data
158(2)
2.2 Graphs of Equations in Two Variables
160(10)
2.3 Graphing Calculators; Solving Equations and Inequalities Graphically
170(9)
2.4 Lines
179(14)
2.5 Modeling: Variation
193(6)
Chapter 2 Review
199(3)
Chapter2 Test
202(10)
FOCUS ON MODELING Fitting Limes to Data
203(9)
3 Functions 212(96)
Chapter Overview
213(1)
3.1 What Is a Function?
214(10)
3.2 Graphs of Functions
224(13)
3.3 Increasing and Decreasing Functions; Average Rate of Change
237(10)
3.4 Transformations of Functions
247(12)
3.5 Quadratic Functions; Maxima and Minima
259(10)
3.6 Combining Functions
269(11)
DISCOVERY PROJECT Iteration and Chaos
278(2)
3.7 One-to-One Functions and Their Inverses
280(9)
Chapter 3 Review
289(4)
Chapter 3 Test
293(15)
FOCUS ON MODELING Modeling with Functions
295(13)
4 Polynomial and Rational Functions 308(74)
Chapter Overview
309(1)
4.1 Polynomial Functions and Their Graphs
310(15)
4.2 Dividing Polynomials
325(8)
4.3 Real Zeros of Polynomials
333(14)
DISCOVERY PROJECT Zeroing in on a Zero
345(2)
4.4 Complex Zeros and the Fundamental Theorem of Algebra
347(11)
4.5 Rational Functions
358(14)
Chapter 4 Review
372(3)
Chapter 4 Teat
375(7)
FOCUS ON MODELING Fitting Polynomial Curves to Data
376(6)
5 Exponential and Logarithmic Functions 382(76)
Chapter Overview
383(1)
5.1 Exponential Functions
384(14)
DISCOVERY PROJECT Exponential Explosion
397(1)
5.2 Logarithmic Functions
398(11)
5.3 Laws of Logarithms
409(6)
5.4 Exponential and Logarithmic Equations
415(12)
5.5 Modeling with Exponential and Logarithmic Functions
427(14)
Chapter 5 Review
441(3)
Chapter 5 Test
444(14)
FOCUS ON MODELING Fitting Exponential and Power Curves to Data
445(13)
6 Systems of Equations and Inequalities 458(54)
Chapter Overview
459(1)
6.1 Systems of Equations
460(9)
6.2 Systems of Linear Equations in Two Variables
469(8)
6.3 Systems of Linear Equations in Several Variables
477(11)
DISCOVERY PROJECT Exact Fit versus Best Fit
486(2)
6.4 Systems of Inequalities
488(7)
6.5 Partial Fractions
495(5)
Chapter 6 Review
500(3)
Chapter 6 Test
503(9)
FOCUS ON MODELING Linear Programming
504(8)
7 Matrices and Determinants 512(60)
Chapter Overview
513(1)
7.1 Matrices and Systems of Linear Equations
514(14)
7.2 The Algebra of Matrices
528(13)
DISCOVERY PROJECT Will the Species Survive?
540(1)
7.3 Inverses of Matrices and Matrix Equations
541(10)
7.4 Determinants and Cramer's Rule
551(12)
Chapter 7 Review
563(3)
Chapter 7 Test
566(6)
FOCUS ON MODELING Computer Graphics
567(5)
8 Conic Sections 572(50)
Chapter Overview
573(1)
8.1 Parabolas
574(10)
DISCOVERY PROJECT Rolling Down a Ramp
583(1)
8.2 Ellipses
584(10)
8.3 Hyperbolas
594(9)
8.4 Shifted Conics
603(9)
Chapter 8 Review
612(3)
Chapter 8 Test
615(7)
FOCUS ON MODELING Conics in Architecture
616(6)
9 Sequences and Series 622(60)
Chapter Overview
623(1)
9.1 Sequences and Summation Notation
624(11)
9.2 Arithmetic Sequences
635(5)
9.3 Geometric Sequences
640(10)
DISCOVERY PROJECT Finding Patterns
649(1)
9.4 Mathematics of Finance
650(7)
9.5 Mathematical Induction
657(7)
9.6 The Binomial Theorem
664(9)
Chapter 9 Review
673(3)
Chapter 9 Test
676(6)
FOCUS ON MODELING Modeling with Recursive Sequences
677(5)
10 Counting and Probability 682
Chapter Overview
683(1)
10.1 Counting Principles
684(5)
10.2 Permutations and Combinations
689(10)
10.3 Probability
699(12)
DISCOVERY PROJECT Small Samples, Big Results
710(1)
10.4 Binomial Probability
711(5)
10.5 Expected Value
716(3)
Chapter 10 Review
719(3)
Chapter 10 Test
722
FOCUS ON MODELING The Monte Carlo Method
723
Answers A1
Index I1
Photo Credits C1


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