Synopses & Reviews
Learn to think mathematically and develop genuine problem-solving skills with Stewart, Redlin, and Watson's COLLEGE ALGEBRA, Fifth Edition. This straightforward and easy-to-use algebra book will help you learn the fundamentals of algebra in a variety of practical ways. The book features new tools to help you succeed, such as learning objectives before each section to prepare you for what you're about to learn, and a list of formulas and key concepts after each section that help reinforce what you've learned. In addition, the book includes many real-world examples that show you how mathematics is used to model in fields like engineering, business, physics, chemistry, and biology.
James Stewart, author of the worldwide, best-selling Calculus texts, along with two of his former Ph.D. students, Lothar Redlin and Saleem Watson, collaborated in writing this text to address a problem they frequently saw in their calculus courses: many students were not prepared to think mathematically but attempted instead to memorize facts and mimic examples. College Algebra was written specifically to help students learn to think mathematically and to develop true problem-solving skills.
About the Author
The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart was most recently Professor of Mathematics at McMaster University, and his research field was harmonic analysis. Stewart was the author of a best-selling calculus textbook series published by Cengage Learning, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts. Lothar Redlin grew up on Vancouver Island, received a Bachelor of Science degree from the University of Victoria, and a Ph.D. from McMaster University in 1978. He subsequently did research and taught at the University of Washington, the University of Waterloo, and California State University, Long Beach. He is currently Professor of Mathematics at The Pennsylvania State University, Abington Campus. His research field is topology. Saleem Watson received his Bachelor of Science degree from Andrews University in Michigan. He did graduate studies at Dalhousie University and McMaster University, where he received his Ph.D. in 1978. He subsequently did research at the Mathematics Institute of the University of Warsaw in Poland. He also taught at The Pennsylvania State University. He is currently Professor of Mathematics at California State University, Long Beach. His research field is functional analysis.
Table of Contents
P. PREREQUISITES. P.1 Modeling the Real World with Algebra. P.2 Real Numbers and Their Properties. P.3 The Real Number Line and Order. P.4 Integer Exponents. P.5 Rational Exponents and Radicals. P.6 Algebraic Expressions. DISCOVERY PROJECT Visualizing a Formula. P.7 Factoring. P.8 Rational Expressions. CHAPTER P Review. CHAPTER P Test. FOCUS ON PROBLEM SOLVING General Principles. 1. EQUATIONS AND INEQUALIITIES. 1.1 Basic Equations. 1.2 Modeling with Equations. DISCOVERY PROJECT Equations Through the Ages. 1.3 Quadratic Equations. 1.4 Complex Numbers. 1.5 Other Types of Equations. 1.6 Inequalities. 1.7 Absolute Value Equations and Inequalities. CHAPTER 1 Review. CHAPTER 1 Test. FOCUS ON MODELING Making the Best Decisions. 2. COORDINATES AND GRAPHS. 2.1 The Coordinate Plane. DISCOVERY PROJECT Visualizing Data. 2.2 Graphs of Equations in Two Variables. 2.3 Graphing Calculators: Solving Equations and Inequalities Graphically. 2.4 Lines. 2.5 Making Models Using Variation. CHAPTER 2 Review. CHAPTER 2 Test. CUMULATIVE REVIEW TEST: Chapters 1 and 2. FOCUS ON MODELING Fitting Lines to Data. 3. FUNCTIONS. 3.1 What is a Function? 3.2 Graphs of Functions. DISCOVERY PROJECT Relations and Functions. 3.3 Getting Information from the Graph of a Function. 3.4 Average Rate of Change of a Function. 3.5 Transformations of Functions. 3.6 Combining Functions. DISCOVERY PROJECT Iteration and Chaos. 3.7 One-to-One Functions and Their Inverses. CHAPTER 3 Review CHAPTER 3 Test. FOCUS ON MODELING Modeling with Functions. 4. POLYNOMIALS AND RATIONAL FUNCTIONS. 4.1 Quadratic Functions and Models. 4.2 Polynomial Functions and Their Graphs. 4.3 Dividing Polynomials. 4.4 Real Zeros of Polynomials. DISCOVERY PROJECT Zeroing in on a Zero. 4.5 Complex Zeros and the Fundamental Theorem of Algebra. 4.6 Rational Functions. CHAPTER 4 Review. CHAPTER 4 Test. FOCUS ON MODELING Fitting Polynomial Curves to Data. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. 5.1 Exponential Functions. DISCOVERY PROJECT Exponential Explosion. 5.2 Logarithmic Functions. 5.3 Laws of Logarithms. 5.4 Exponential and Logarithmic Equations. 5.5 Modeling with Exponential and Logarithmic Functions. CHAPTER 5 Review. CHAPTER 5 Test. CUMULATIVE REVIEW TEST: Chapters 3, 4, and 5. FOCUS ON MODELING Fitting Exponential and Power Curves to Data. 6. SYSTEMS OF EQUATIONS AND INEQUALITIES. 6.1 Systems of Equations. 6.2 Systems of Linear Equations in Two Variables. 6.3 Systems of Linear Equations in Several Variables. DISCOVERY PROJECT Best Fit Versus Exact Fit. 6.4 Partial Fractions. 6.5 Systems of Inequalities. CHAPTER 6 Review. CHAPTER 6 Test. FOCUS ON MODELING Linear Programming. 7. MATRICES AND DETERMINANTS. 7.1 Matrices and Systems of Linear Equations. 7.2 The Algebra of Matrices. DISCOVERY PROJECT Will the Species Survive? 7.3 Inverses of Matrices and Matrix Equations. 7.4 Determinants and Cramers Rule. CHAPTER 7 Review. CHAPTER 7 Test. FOCUS ON MODELING Computer Graphics. 8. CONIC SECTIONS. 8.1 Parabolas. DISCOVERY PROJECT Rolling Down a Ramp. 8.2 Ellipses. 8.3 Hyperbolas. 8.4 Shifted Conics. CHAPTER 8 Review. CHAPTER 8 Test. CUMULATIVE REVIEW TEST: Chapters 6, 7, and 8. FOCUS ON MODELING Conics in Architecture. 9. SEQUENCES AND SERIES. 9.1 Sequences and Summation Notation. 9.2 Arithmetic Sequences. 9.3 Geometric Sequences. DISCOVERY PROJECT Finding Patterns. 9.4 Mathematics of Finance. 9.5 Mathematical Induction. 9.6 The Binomial Theorem. CHAPTER 9 Review. CHAPTER 9 Test. FOCUS ON MODELING Modeling with Recursive Sequences. 10. COUNTING AND PROBABILITY. 10.1 Counting Principles. 10.2 Permutations and Combinations. 10.3 Probability. DISCOVERY PROJECT Small Samples, Big Results. 10.4 Binomial Probability. 10.5 Expected Value. CHAPTER 10 Review. CHAPTER 10 Test. CUMULATIVE REVIEW TEST: Chapters 9 and 10. FOCUS ON MODELING The Monte Carlo Method.