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Algebra and Trigonometry (with Video Skillbuilder CD-ROM and 1pass for Ilrn Tutorial)
Synopses & Reviews
James Stewart, the 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 book to address a problem they frequently saw in their calculus courses. Many students were not prepared to "think mathematically" but attempted to memorize facts and mimic examples. ALGEBRA AND TRIGONOMETRY was designed specifically to help readers learn to think mathematically and to develop true problem-solving skills. Patient, clear, and accurate, the text consistently illustrates how useful and applicable mathematics is to real life. The new book follows the successful approach taken in the authors' previous books, COLLEGE ALGEBRA, Third Edition, and PRECALCULUS, Third Edition.
Book News Annotation:
This textbook begins with graphs and functions, introduces trigonometry through both the right triangle and unit circle approaches, and ends with systems of equations, conic sections, sequences, series, counting, and probability. The second edition adds more emphasis on modeling the real world and a chapter on polar coordinates and vectors. The CD-ROM contains video instruction.
Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)
Book News Annotation:
This textbook begins with graphs and functions, introduces trigonometry through both the right triangle and unit circle approaches, and ends with systems of equations, conic sections, sequences, series, counting, and probability. The second edition adds more emphasis on modeling the real world and a chapter on polar coordinates and vectors. The CD-ROM contains video instruction. Annotation Â©2006 Book News, Inc., Portland, OR (booknews.com)
This best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, so that when students finish the course, they have a solid foundation in the principles of mathematical thinking. This comprehensive, evenly paced book provides complete coverage of the function concept and integrates substantial graphing calculator materials that help students develop insight into mathematical ideas. The authors' attention to detail and clarity, as in James Stewart's market-leading Calculus text, is what makes this text the market leader.
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. Modeling the Real World. Real Numbers. Integer Exponents. Rational Exponents and Radicals. Algebraic Expressions. Discovery Project: Visualizing a Formula. Factoring Algebraic Expressions. Rational Expressions. Chapter P Review. Chapter P Test. Focus on Problem Solving: General Principles. 1. EQUATIONS AND INEQUALITIES. Basic 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. Chapter 1 Review. Chapter 1 Test. Focus on Modeling: Making the Best Decisions. 2. COORDINATES AND GRAPHS. The Coordinate Plane. Discovery Project: Visualizing Data. Graphs of Equations in Two Variables. Graphing Calculators: Solving Equations and Inequalities Graphically. Lines.Modeling: Variation. Chapter 2 Review. Chapter 2 Test. Focus on Modeling: Fitting Lines to Data. 3. FUNCTIONS. What is a Function? Graphs of Functions. Discovery Project: Relations and 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. Chapter 3 Review. Chapter 3 Test. Focus on Modeling: Modeling With Functions. 4. POLYNOMIAL AND RATIONAL FUNCTIONS. 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. Chapter 4 Review. Chapter 4 Test. Focus on Modeling: Fitting Polynomial Curves to Data. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Discovery Project: Exponential Explosion. Logarithmic Functions. Laws of Logarithms. Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions. Chapter 5 Review. Chapter 5 Test. Focus on Modeling: Fitting Exponential and Power Curves to Data. 6. TRIGONOMETRIC FUNCTIONS OF ANGLES. Angle Measure. Trigonometry of Right Triangles. Trigonometric Functions of Angles. Discovery Project: Similarity. The Law of Sines. The Law of Cosines. Chapter 6 Review. Chapter 6 Test. Focus on Modeling: Surveying. 7. TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS. The Unit Circle. Trigonometric Functions of Real Numbers. Trigonometric Graphs. Discovery Project: Predator-Prey Models. More Trigonometric Graphs. Modeling Harmonic Motion. Chapter 7 Review. Chapter 7 Test. Focus on Modeling: Fitting Sinusoidal Curves to Data. 8. ANALYTIC TRIGONOMETRY. Trigonometric Identities. Addition and Subtraction Formulas. Double-Angle, Half-Angle, and Sum-Product Identities. Inverse Trigonometric Functions. Discovery Project:Where to Sit at the Movies. Trigonometric Equations. Chapter 8 Review. Chapter 8 Test. Focus on Modeling: Traveling and Standing Waves. 9. POLAR COORDINATES AND VECTORS. Polar Coordinates. Graphs of Polar Equations. Polar Form of Complex Numbers; DeMoivre's Theorem. Discovery Project: Fractals. Vectors. The Dot Product. Discovery Project: Sailing Against the Wind. Chapter 9 Review. Chapter 9 Test. Focus on Modeling: Mapping the World. 10. SYSTEMS OF EQUATIONS AND INEQUALITIES. Systems of Equations. Systems of Linear Equations in Two Variables. Systems of Linear Equations in Several Variables. Discovery Project: Best Fit versus Exact Fit. Systems of Linear Equations: Matrices. The Algebra of Matrices. Discovery Project: Will the Species Survive? Inverses of Matrices and Matrix Equations. Discovery Project: Computer Graphics I. Determinants and Cramer's Rule. Partial Fractions. Systems of Inequalities. Chapter 10 Review. Chapter 10 Test. Focus on Modeling: Linear Programming. 11. ANALYTIC GEOMETRY. Parabolas. Ellipses. Hyperbolas. Discovery Project: Conics in Architecture. Shifted Conics. Rotation of Axes. Discovery Project: Computer Graphics II. Polar Equations of Conics. Plane Curves and Parametric Equations. Chapter 11 Review. Chapter 11 Test. Focus on Modeling: The Path of a Projectile. 12. SEQUENCES AND SERIES. Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Discovery Project: Finding Patterns. Mathematics of Finance. Mathematical Induction. The Binomial Theorem. Chapter 12 Review. Chapter 12 Test. Focus on Modeling: Modeling with Recursive Sequences. 13. COUNTING AND PROBABILITY. Counting Principles. Permutations and Combinations. Probability. Discovery Project: Small Samples, Big Results. Binomial Probability. Expected Value. Chapter 13 Review. Chapter 13 Test. Focus on Modeling: The Monte Carlo Method.
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