Precalculus

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Overview

PRECALCULUS prepares learners for calculus and the rigors of that course, having been written by teachers who have taught the courses and seen where learners need help—and where other texts have come up short. The text features precise definitions and exposition, carefully crafted pedagogy, and a strong emphasis on algebraic, transcendental, and trigonometric functions. To show readers how important and relevant precalculus topics are to their future coursework, an optional Looking Ahead to Calculus feature appears in each chapter. The varied examples and exercises include many that encourage readers to use and understand graphs, as opposed to simply draw them, providing additional sound preparation for calculus.

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Product Details

  • ISBN-13: 9780495826620
  • Publisher: Cengage Learning
  • Publication date: 2/6/2012
  • Series: New 1st Editions in Mathematics Series
  • Edition description: New Edition
  • Pages: 1024
  • Product dimensions: 8.80 (w) x 11.00 (h) x 1.40 (d)

Meet the Author

Karla Neal received two degrees in mathematics from Louisiana State University and has been an instructor in the department of Mathematics for 31 years. During that time, she has served as the coordinator for College Trigonometry for more than 15 years. She has received three campus-wide teaching awards, and has served as a faculty advisor for several Christian campus organizations. Karla is an avid fan of the LSU Tigers. When she is not on campus, she is very active in her church, Healing Place Church in Baton Rouge, and can often be found on the golf course. At home, there are two dogs, Winston and Josie, waiting patiently.

R. David Gustafson is Professor Emeritus of Mathematics at Rock Valley College in Illinois and has also taught extensively at Rockford College and Beloit College. He is coauthor of several best-selling mathematics textbooks, including Gustafson/Frisk/Hughes' COLLEGE ALGEBRA, Gustafson/Karr/Massey's BEGINNING ALGEBRA, INTERMEDIATE ALGEBRA, BEGINNING AND INTERMEDIATE ALGEBRA, BEGINNING AND INTERMEDIATE ALGEBRA: A COMBINED APPROACH, and the Tussy/Gustafson and Tussy/Gustafson/Koenig developmental mathematics series. His numerous professional honors include Rock Valley Teacher of the Year and Rockford's Outstanding Educator of the Year. He has been very active in AMATYC as a Midwest Vice-president and has been President of IMACC, AMATYC's Illinois affiliate. He earned a Master of Arts from Rockford College in Illinois, as well as a Master of Science from Northern Illinois University.

Jeff Hughes has taught the college algebra course continually for the past 20 years, and his firsthand experience with students lends itself to the innovative ideas he has brought to the text. He has led the way for the addition of the new features and the revised content in COLLEGE ALGEBRA, 10E. He teaches at Hinds Community College in Mississippi.

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Table of Contents

R. BASIC CONCEPTS. Linear Equations and Applications. Complex Numbers. Quadratic Equations and Applications. Other Types of Equations. Inequalities. The Rectangular Coordinate System. Equations of Lines. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 1. GRAPHS AND FUNCTIONS. Graphs of Equations. Functions and Function Notation. Graphs of Functions. Basic Graphs. Transformations of Graphs. Operations on Functions. Inverse Functions. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 2. POLYNOMIAL AND RATIONAL FUNCTIONS. Quadratic Functions. Polynomial Functions. Rational Zeros of Polynomial Functions. Roots of Polynomial Equations. Rational Functions. Polynomial and Rational Inequalities. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions, Graphs, and Applications. Applications of Exponential Functions. Logarithmic Functions and Their Graphs. Applications of Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 4. TRIGONOMETRIC FUNCTIONS. Angles and Their Measurement. The Unit Circle and Trigonometric Functions. Trigonometric Functions of Any Angle; Fundamental Identities. Graphs of the Sine and Cosine Functions. Graphs of the Tangent, Cotangent, Secant and Cosecant Functions. Regression and Other Graphs Involving Trigonometric Functions. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 5. ANALYTIC TRIGONOMETRY. Inverse Trigonometric Functions. Inverse Cotangent, Secant, and Cosecant Functions (Optional). Verifying Trigonometric Identities. Sum and Difference Formulas. Double-Angle, Power-Reduction, Half-Angle Formulas. Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations I. Trigonometric Equations II. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 6. APPLICATIONS; OBLIQUE TRIANGLES. Solving Right Triangles. More Right Triangle Applications. Law of Sines. Law of Cosines. Area of Triangles. Angular and Linear Velocity—Circular Motion. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 7. POLAR COORDINATES; VECTORS. Polar Coordinates. Polar Equations and Graphs. Complex Plane; Polar Form of Complex Numbers; DeMoivre's Theorem. Vectors. Dot Product. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 8. LINEAR SYSTEMS AND MATRICES. Systems of Linear Equations. Gaussian Elimination and Matrix Methods. Matrix Algebra. Matrix Inversion. Determinants. Partial Fractions. Graphs of Linear Inequalities. Linear Programming (available on website). Chapter Summary. Chapter Test. Looking Ahead to Calculus. 9. CONIC SECTIONS AND QUADRATIC SYSTEMS. The Circle and the Parabola. The Ellipse. The Hyperbola. Solving Non-linear Systems of Equations. Plane Curves and Parametric Equations. Conic Sections in Polar Coordinates. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 10. NATURAL NUMBER FUNCTIONS AND PROBABILITY. The Binomial Theorem. Sequences, Series, and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. Permutations and Combinations (available on website). Probability (available on website). Chapter Summary. Chapter Test. Looking Ahead to Calculus. 11. INTRODUCTION TO CALCULUS (available on website). Limits. Properties of Limits. Limits and Continuity. Average Rate of Change. Tangents and Derivatives. Area and Integrals. Chapter Summary. Chapter Test. APPENDIX. Sets of Real Numbers. Integer Exponents and Scientific Notation. Radicals and Rational Exponents. Polynomials. Factoring Polynomials. Rational Expressions.

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