Synopses & Reviews
Based on years of experience teaching and writing supplemental materials for more traditional precalculus texts, Reva Narasimhan takes a functions-focused approach to teaching and learning algebra and trigonometry concepts. This new series builds up relevant concepts using functions as a unifying theme, repeating and expanding on connections to basic functions. Visualization and analysis motivate the functions-based approach, enabling students to better retain the material for use in later calculus courses. Highlights of this new book include:
Synopsis
Based on years of experience teaching and writing supplemental materials for more traditional precalculus texts, Reva Narasimhan takes a functions-focused approach to teaching and learning algebra and trigonometry concepts. This new series builds up relevant concepts using functions as a unifying theme, repeating and expanding on connections to basic functions. Visualization and analysis motivate the functions-based approach, enabling students to better retain the material for use in later calculus courses.
About the Author
Revathi Narasimhan received her Ph.D. in Applied Mathematics from the University of Maryland at College Park. She grew up in Mesa, Arizona and received her undergraduate degree at Arizona State University. She is currently on the faculty of the Mathematics Department at Kean University in Union, New Jersey.Professionally trained to apply the principles of analysis and algebra, she is keen on helping her students understand the "big picture" concepts in mathematics, whether at the graduate or at the undergraduate level. In addition to this textbook, she has written scholarly articles for academic journals and has written technology supplements for other textbooks. She and her husband, a research microbiologist, have two sons. Reva likes to garden and sew, and is an avid reader.
Table of Contents
Chapters 1-11 conclude with a Chapter Summary and Review Exercises. P. Algebra and Geometry Review P.1 The Real Number System P.2 Integer Exponents and Scientific Notation P.3 Roots, Radicals, and Rational Exponents P.4 Polynomials P.5 Factoring P.6 Rational Expressions P.7 Geometry Formulas P.8 Solving Basic Equations 1. Functions, Graphs, and Applications 1.1 Functions 1.2 Graphs of Functions 1.3 Linear Functions 1.4 Modeling with Linear Functions; Variation 1.5 Intersections of Lines and Linear Inequalities 2. More About Functions and Coordinate Geometry 2.1 Coordinate Geometry: Distance, Midpoints, and Circles 2.2 The Algebra of Functions 2.3 Transformations of the Graph of Functions 2.4 Symmetry and Other Properties of Functions 2.5 Equations and Inequalities Involving Absolute Value 2.6 Piecewise-Defined Functions 3. Quadratic Functions 3.1 Graphs of Quadratic Functions 3.2 Quadratic Equations 3.3 Complex Numbers and Quadratic Equations 3.4 Quadratic Inequalities 3.5 Equations Reducible to Quadratic Form; Rational and Radical Equations 4. Polynomial and Other Functions 4.1 Graphs of Polynomial Functions 4.2 More on Graphs of Polynomial Functions and Models 4.3 Division of Polynomials; The Remainder and Factor Theorems 4.4 Real Zeros of Polynomials; Solutions of Equations 4.5 The Fundamental Theorem of Algebra; Complex Zeros 4.6 Rational Functions 4.7 Polynomial and Rational Inequalities 5. Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions 5.3 Logarithmic Functions 5.4 Properties of Logarithms 5.5 Exponential and Logarithmic Equations 5.6 Exponential, Logistic, and Logarithmic Models 6. Trigonometric Functions 6.1 Angles and Their Measures 6.2 Trigonometric Functions Using the Right Triangle 6.3 Trigonometric Functions of Any Angle: Unit Circle Definition 6.4 Graphs of the Sine and Cosine Functions 6.5 Graphs of the Other Trigonometric Functions 6.6 Inverse Trigonometric Functions 7. Trigonometric Identities and Equations 7.1 Verifying Identities 7.2 Sum and Difference Identities 7.3 Multiple Angle Identities; Sum and Product Identities 7.4 Trigonometric Equations 8. Additional Topics in Trigonometry 8.1 The Law of Sines 8.2 The Law of Cosines 8.3 Vectors 8.4 Trigonometric Form of a Complex Number 9. Analytic Geometry 9.1 The Parabola 9.2 The Ellipse 9.3 The Hyperbola 9.4 General Form of Conic Sections; Rotation 9.5 Polar Coordinates and Graphs 9.6 Polar Equations of Conic Sections 9.7 Parametric Equations 10. Systems of Equations and Linear Inequalities 10.1 Systems of Linear Equations and Inequalities in Two Variables 10.2 Systems of Linear Equations in Three Variables 10.3 Solving Systems of Equations with Matrices 10.4 Operations with Matrices 10.5 Matrices and Inverses 10.6 Determinants and Cramer's Rule 10.7 Partial Fractions 10.8 Systems of Nonlinear Equations 11. More Topics in Algebra 11.1 Sequences 11.2 Sums of Terms of Sequences 11.3 General Sequences and Series 11.4 Counting Methods 11.5 Probability 11.6 The Binomial Theorem 11.7 Mathematical Induction Appendix. A TI-84 Keystroke Guide A.1 Keys on Your Calculator A.2 Getting Started A.3 Editing Your Work A.4 Entering Common Expressions A.5 Evaluating Functions A.6 Building Tables A.7 Graphing Linear, Quadratic, and Piecewise-Defined Functions A.8 Solving Equations A.9 Finding Maximum and Minimum of a Function A.10 Graphing Polynomial and Rational Functions and Inequalities A.11 Complex Numbers A.12 Fitting Curves to Data A.13 Matrices A.14 Sequences and Series