College Algebra

James Stewart received the M.S. degree from Stanford University and the Ph.D. from the University of Toronto. After two years as a postdoctoral fellow at the University of London, he became Professor of Mathematics at McMaster University. His research has been in harmonic analysis and functional analysis. Stewart’s books include a series of high school textbooks as well as a best-selling series of calculus textbooks published by Cengage Learning. He is also co-author, with Lothar Redlin and Saleem Watson, of a series of college algebra and precalculus textbooks. Translations of his books include those into Spanish, Portuguese, French, Italian, Korean, Chinese, Greek, Indonesian and Japanese. A talented violinist, Stewart was concertmaster of the McMaster Symphony Orchestra for many years and played professionally in the Hamilton Philharmonic Orchestra. He has given more than 20 talks worldwide on mathematics and music. Stewart was named a Fellow of the Fields Institute in 2002 and was awarded an honorary D.Sc. in 2003 by McMaster University. The library of the Fields Institute is named after him. The James Stewart Mathematics Centre was opened in October, 2003, at McMaster University. The late Lothar Redlin grew up on Vancouver Island and received a bachelor of science degree from the University of Victoria and a Ph.D. from McMaster University. He subsequently did research and taught at the University of Washington and the University of Waterloo as well as California State University, Long Beach. He was most recently a professor of mathematics at The Pennsylvania State University, Abington Campus. His research focused on topology. Dr. Redlin was a valued co-author for Dr. Stewart's best-selling calculus textbook series and his popular precalculus, college algebra and trigonometry texts. Saleem Watson received his bachelor of science degree from Andrews University in Michigan. He completed his graduate studies at Dalhousie University and McMaster University, where he received his Ph.D. Dr. Watson conducted subsequently research at the Mathematics Institute of the University of Warsaw in Poland. He taught mathematics at Pennsylvania State University before serving at California State University, Long Beach, where he is currently professor emeritus. Dr. Watson's research encompasses the field of functional analysis. Dr. Watson is an important co-author for Dr. Stewart's best-selling calculus textbook series as well as his popular precalculus, college algebra and trigonometry texts.

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• Preface.To the Student.Prologue: Principles of Problem Solving.P. PREREQUISITES. P.1 Modeling the Real-World with Algebra. P.2 The Real Numbers. P.3 Integer Exponents and Scientific Notation. P.4 Rational Exponents and Radicals. P.5 Algebraic Expressions. P.6 Factoring. P.7 Rational Expressions. P.8 Solving Basic Equations. P.9 Modeling with Equations. Chapter P Review. Chapter P Test.FOCUS ON MODELING: Making the Best Decisions.1. EQUATIONS AND GRAPHS.1.1 The Coordinate Plane. 1.2 Graphs of Equations in Two Variables; Circles. 1.3 Lines.1.4 Solving Quadratic Equations. 1.5 Complex Numbers. 1.6 Solving Other Types of Equations. 1.7 Solving Inequalities. 1.8 Solving Absolute Value Equations and Inequalities. 1.9 Solving Equations and Inequalities Graphically. 1.10 Modeling Variations. Chapter 1 Review. Chapter 1 Test.FOCUS ON MODELING: Fitting Lines to Data.2. FUNCTIONS.Chapter Overview.2.1 Functions. 2.2 Graphs of Functions. 2.3 Getting Information from the Graph of a Function. 2.4 Average Rate of Change of a Function. 2.5 Linear Functions and Models.2.6 Transformations of Functions. 2.7 Combining Functions. 2.8 One-to-One Functions and Their Inverses. Chapter 2 Review. Chapter 2 Test.FOCUS ON MODELING: Modeling with Functions.3. POLYNOMIAL AND RATIONAL FUNCTIONS.Chapter Overview.3.1 Quadratic Functions and Models. 3.2 Polynomial Functions and Their Graphs. 3.3 Dividing Polynomials. 3.4 Real Zeros of Polynomials. 3.5 Complex Zeros and the Fundamental Theorem of Algebra. 3.6 Rational Functions. 3.7 Polynomial and Rational Inequalities. Chapter 3 Review. Chapter 3 Test.FOCUS ON MODELING: Fitting Polynomial Curves to Data.4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.Chapter Overview.4.1 Exponential Functions. 4.2 The Natural Exponential Function. 4.3 Logarithmic Functions. 4.4 Laws of Logarithms. 4.5 Exponential and Logarithmic Equations. 4.6 Modeling with Exponential Functions. 4.7 Logarithmic Scales. Chapter 4 Review. Chapter 4 Test.FOCUS ON MODELING: Fitting Exponential and Power Curves to Data.5. SYSTEMS OF EQUATIONS AND INEQUALITIES.5.1 Systems of Linear Equations in Two Variables. 5.2 Systems of Linear Equations in Several Variables. 5.3 Partial Fractions. 5.4 Systems of Nonlinear Equations. 5.5 Systems of Inequalities. Chapter 5 Review. Chapter 5 Test.FOCUS ON MODELING: Linear Programming.6. MATRICES AND DETERMINANTS.6.1 Matrices and Systems of Linear Equations. 6.2 The Algebra of Matrices. 6.3 Inverses of Matrices and Matrix Equations. 6.4 Determinants and Cramer's Rule. Chapter 6 Review. Chapter 6 Test.FOCUS ON MODELING: Computer Graphics.7. CONIC SECTIONS.7.1 Parabolas. 7.2 Ellipses. 7.3 Hyperbolas. 7.4 Shifted Conics. Chapter 7 Review.Chapter 7 Test.FOCUS ON MODELING: Conics in Architecture.8. SEQUENCES AND SERIES.8.1 Sequences and Summation Notation. 8.2 Arithmetic Sequences. 8.3 Geometric Sequences. 8.4 Mathematics of Finance. 8.5 Mathematical Induction. 8.6 The Binomial Theorem. Chapter 8 Review. Chapter 8 Test.FOCUS ON MODELING: Modeling with Recursive Sequences.9. COUNTING AND PROBABILITY.9.1 Counting. 9.2 Probability. 9.3 Binomial Probability. 9.4 Expected Value. Chapter 9 Review. Chapter 9 Test.FOCUS ON MODELING: The Monte Carlo Method.APPENDIX A: Calculations and Significant Figures.APPENDIX B: Graphing with a Graphing Calculator.APPENDIX C: Using the TI-83/84 Graphing Calculator.