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College Algebra: Understanding Functions, a Graphing Approach with CDROM
Synopses & ReviewsPublisher Comments:These experienced authors have been praised for their indepth explanations and their commitment to avoiding a cookbook approach. Their text addresses three critical issues in teaching college algebra: poor student preparation, the need for thoughtful integration of the graphing calculator, and poor student study skills. Their texts have a strong reputation built on mathematically sound presentation, excellent applications, and on challenging students to develop algebraic, graphical, and verbal mathematical skills. Goodman and Hirsch help students go beyond the mechanics of mathematics to developing a coherent strategy to solving problems.
Book News Annotation:Emphasizing visualization, problem solving, and mathematical modeling, this textbook covers the basics of algebra, equations and inequalities, graphs, polynomials, rational and radical functions, exponential and logarithmic functions, systems of linear equations and inequalities, conic sections and nonlinear systems, and sequences and series. A companion CDROM contains eight hours of video instruction and tutorial exercises. The authors are affiliated with Queens College and Rutgers University.
Annotation ©2004 Book News, Inc., Portland, OR (booknews.com) About the AuthorDr. Arthur Goodman (Ph.D., Yeshiva University) currently teaches in the mathematics department at Queens College of the City University of New York.
Table of Contents1. ALGEBRA: THE FUNDAMENTALS. The Real Numbers. Operations with Real Numbers. Polynomials. Rational Expressions. Exponents and Radicals. The Complex Numbers. Chapter Summary. Review Exercises. Practice Test. 2. EQUATIONS AND INEQUALITIES. FirstDegree Equations and Inequalities in One Variable. Absolute Value Equations and Inequalities. Quadratic Equations. Radical Equations: Equations Reducible to Quadratic Form. Quadratic and Rational Inequalities. Substitution. Chapter Summary. Review Exercises. Practice Test. 3. FUNCTIONS AND GRAPHS: PART I. The Cartesian Coordinate System: Graphing Straight Lines Functions and Circles. Slope. Equations of a Line. Relations and Functions. Function Notation. Relating Equations to Their Graphs. Introduction to Graph Sketching: Symmetry. Chapter Summary. Review Exercises. Practice Test. 4. FUNCTIONS AND GRAPHS: PART II. Basic Graphing Principles. More Graphing Principles: Types of Functions. Extracting Functions from RealLife Situations. Quadratic Functions. Operations on Functions. Inverse Functions. Chapter Summary. Review Exercises. Practice Test. 5. POLYNOMIAL, RATIONAL AND RADICAL FUNCTIONS. Polynomial Functions. More Polynomial Functions and Mathematical Models. Polynomial Division, Roots of Polynomial Equations; The Remainder and Factor Theorems. Roots of Polynomial Equations (continued); The Rational Root Theorem and Descartes's Rule of Signs. Rational Functions. Radical Functions. Variation. Chapter Summary. Review Exercises. Practice Test. 6. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Logarithmic Functions. Properties of Logarithms: Logarithmic Equations. Common and Natural Logarithms: Exponential Equations and Change of Base. Applications. Chapter Summary. Review Exercises. Practice Test. 7. SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES. Elimination and Substitution: 2 X 2 Linear Systems. Elimination and Gaussian Elimination: 3 X 3 Linear Systems. Solving Linear Systems Using Augmented Matrices. The Algebra of Matrices. Solving Linear. Systems Using Matrix Inverses. Determinants and Cramer's Rule: 2 X 2 and 3 X 3 Systems. Properties of Determinants. Systems of Linear Inequalities. An Introduction to Linear Programming: Geometric Solutions. Chapter Summary. Review Exercises. Practice Test. 8. CONIC SECTIONS AND NONLINEAR SYSTEMS. Conic Sections: Circles. The Parabola. The Ellipse. The Hyperbola. Identifying Conic Sections: Degenerate Forms. Nonlinear Systems of Equations and Inequalities. Chapter Summary. Review Exercises. Practice Test. 9. SEQUENCE, SERIES AND RELATED TOPICS. Sequences. Series and Sigma Notation. Arithmetic Sequences and Series. Geometric Sequences and Series. Mathematical Induction. Permutations and Combinations. Probability. The Binomial Theorem. Chapter Summary. Review Exercises. Practice Test.
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