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

by Stewart, James; Redlin, Lothar; Watson, Saleem

• ISBN13: 9780534405991
• ISBN10: 0534405991
• Edition: 4th
• Format: Hardcover
• Copyright: 2003-11-06
• Publisher: Brooks Cole

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