Synopses & Reviews
The Fourth Edition of Yoshiwara and Yoshiwara's MODELING, FUNCTIONS, AND GRAPHS: ALGEBRA FOR COLLEGE STUDENTS includes content found in a typical algebra course, along with introductions to curve-fitting and display of data. Yoshiwara and Yoshiwara focus on three core themes throughout their textbook: Modeling, Functions, and Graphs. In their work of modeling and functions, the authors utilize the Rule of Four, which is that all problems should be considered using algebraic, numerical, graphical, and verbal methods. The authors motivate students to acquire the skills and techniques of algebra by placing them in the context of simple applications that use real-life data.
Synopsis
Popular with and respected by students interested in a Modeling Approach, Graphing, or Graphing Calculators, this book incorporates the benefits of technology and the philosophy of the reform movement into intermediate algebra. In keeping with the NCTM and AMATYC standards, the authors introduce the techniques of algebra in the context of simple applications. Early and consistent emphasis on functions and graphing helps to develop mathematical models, and graphing calculators are incorporated wherever possible.
About the Author
Kathy Yoshiwara was born in Derby in the UK and grew up in Richmond, Virginia. She attended Michigan State University, where she studied Greek and mathematics. She did graduate work at UCLA and earned an MA in mathematics in 1977. She left UCLA in 1979 to join the faculty at Pierce College, where she has been teaching ever since, except for the 1988-1999 academic year, when she taught at Barnsley College in Yorkshire (northern England) on a Fulbright teaching exchange. She is the author or co-author of three mathematics textbooks and is a member of the Calculus Consortium for Higher Education, where she is part of the writing team for their Precalculus text. She is a member of the MAA (Mathematical Association of America) and currently serves on the Committee for Curriculum Renewal and the First Two Years (CRAFTY). In 1996 she received the Award for Distinguished College or University Teaching of Mathematics from the Southern California Section of the MAA. She is married to Bruce Yoshiwara and benefits from his expertise in all things mathematical.Bruce Yoshiwara has taught full-time at L.A. Pierce College since 1989 (except for the 1998-1999 academic year, when he and his wife Katherine Yoshiwara both had Fulbright Teacher Exchange positions at Barnsley College, England). He is co-author (Katherine is the principal author) of three algebra and pre-algebra textbooks. He serves on the Mathematical Association of American (MAA) Committee on Computers in Mathematics Education and is a consultant for Project NExT (New Experiences in Teaching). Bruce is editor of the Pierce Math Department newsletter and maintains the department web page.
Table of Contents
1. LINEAR MODELS Some Examples of Linear Models / Using A Graphing Calculator / Slope / Equations of Lines / Lines of Best Fit / Additional Properties of Lines 2. APPLICATIONS OF LINEAR MODELS Systems of Linear Equations in Two Variables / Solution of Systems by Algebraic Methods / Systems of Linear Equations in Three Variables / Solution of Linear Systems Using Matrices / Linear Inequalities in Two Variables 3. QUADRATIC MODELS Extraction of Roots / Some Examples of Quadratic Models / Solving Quadratic Equations by Factoring / Graphing Parabolas; Special Cases / Completing the Square / Quadratic Formula 4. APPLICATIONS OF QUADRATIC MODELS Graphing Parabolas: the General Case / Curve Fitting / Problem Solving / Quadratic Inequalities / Solving Quadratic Inequalities Algebraically 5. FUNCTIONS AND THEIR GRAPHS Definitions and Notation / Graphs of Functions / Some Basic Graphs / Domain and Range / Variation / Functions as Mathematical Models / 6. POWERS AND ROOTS Integer Exponents / Roots and Radicals / Rational Exponents / The Distance and Midpoint Formulas / Working with Radicals / Radical Equations 7. EXPONENTIAL MODELS Exponential Growth and Decay / Exponential Functions / Logarithms / Logarithmic Functions / Properties of Logarithms / The Natural Base 8. POLYNOMIAL AND RATIONAL FUNCTIONS Polynomial Functions / Graphing Polynomial Functions / Rational Functions / Operations on Algebraic Fractions / More Operations on Algebraic Fractions / Equations That Include Algebraic Fractions 9. SEQUENCES AND SERIES Sequences / Arithmetic and Geometric Sequences / Series / Sigma Notation and Infinite Geometric Series / The Binomial Expansion 10. MORE ABOUT FUNCTIONS Transformations of Functions / Using Function Notation / Inverse Functions / More about Modeling / Joint Variation 11. MORE ABOUT GRAPHS Conic Sections / Translated Conics / Systems of Quadratic Equations / Linear Programming / Displaying Data / APPENDIX A: REVIEW TOPICS / APPENDIX B: THE NUMBER SYSTEM / APPENDIX