PRECALCULUS GRAPHS & MODELS 3/

3. Auflage 2008
ISBN: 978-0-07-722129-4
Verlag: MCGRAW HILL BOOK CO

Buch, Englisch, 1184 Seiten, Format (B × H): 208 mm x 259 mm, Gewicht: 2354 g

The Barnett Graphs & Models series in college algebra and precalculus maximizes student comprehension by emphasizing computational skills, real-world data analysis and modeling, and problem solving rather than mathematical theory. Many examples feature side-by-side algebraic and graphical solutions, and each is followed by a matched problem for the student to work. This active involvement in the learning process helps students develop a more thorough understanding of concepts and processes. A hallmark of the Barnett series, the function concept serves as a unifying theme. A major objective of this book is to develop a library of elementary functions, including their important properties and uses. Employing this library as a basic working tool, students will be able to proceed through this course with greater confidence and understanding as they first learn to recognize the graph of a function and then learn to analyze the graph and use it to solve the problem. Applications included throughout the text give the student substantial experience in solving and modeling real world problems in an effort to convince even the most skeptical student that mathematics is really useful.

Autoren/Hrsg.

Barnett, Raymond

Ziegler, Michael

Byleen, Karl

Sobecki, David

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Elementare Algebra

Inhaltsverzeichnis

CHAPTER 1 FUNCTIONS, GRAPHS, AND MODELS1-1 Using Graphing Utilities1-2 Functions1-3 Functions: Graphs and Properties1-4 Functions: Graphs and Transformations1-5 Operations on Functions; Composition1-6 Inverse FunctionsChapter 1 ReviewChapter 1 Group Activity: Mathematical Modeling–Choosing a Long Distance Calling PlanCHAPTER 2 MODELING WITH LINEAR AND QUADRATIC FUNCTIONS2-1 Linear Functions2-2 Linear Equations and Models2-3 Quadratic Functions2-4 Complex Numbers2-5 Quadratic Equations and Models2-6 Additional Equation Solving Techniques2-7 Solving InequalitiesChapter 2 ReviewChapter 2 Group Activity: Mathematical Modeling in Population StudiesCumulative Review Exercise for Chapters 1 and 2CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS3-1 Polynomial Functions And Models3-2 Polynomial Division3-3 Real Zeros and Polynomial Inequalities3-4 Complex Zeros and Rational Zeros of Polynomials3-5 Rational Functions and Inequalities3-6 Variation and ModelingChapter 3 ReviewChapter 3 Group Activity: Interpolating PolynomialsCHAPTER 4 MODELING WITH EXPONENTIAL AND LOGARITHMIC FUNCTIONS4-1 Exponential Functions4-2 Exponential Models4-3 Logarithmic Functions4-4 Logarithmic Models4-5 Exponential and Logarithmic EquationsChapter 4 ReviewChapter 4 Group Activity: Comparing Regression ModelsCumulative Review Exercise for Chapters 3 and 4CHAPTER 5 TRIGONOMETRIC FUNCTIONS5-1 Angles and Their Measure5-2 Trigonometric Functions: A Unit Circle Approach5-3 Solving Right Triangles5-4 Properties of Trigonometric Functions5-5 More General Trigonometric Functions and and Models5-6 Inverse Trigonometric FunctionsChapter 5 ReviewChapter 5 Group Activity: A Predator-Prey Analysis Involving Mountain Lions and DeerCHAPTER 6 TRIGONOMETRIC IDENTITIES AND CONDITIONAL EQUATIONS6-1 Basic Identities and Their Use6-2 Sum, Difference, and Cofunction Identities6-3 Double-Angle and Half-Angle Identities6-4 Product-Sum and Sum-Product Identities6-5 Trigonometric EquationsChapter 6 ReviewChapter 6 Group Activity: From M sin Bt + N cos Bt to A sin (Bt + C) - A Harmonic Analysis ToolCHAPTER 7 ADDITIONAL TOPICS IN TRIGONOMETRY7-1 Law of Sines7-2 Law of Cosines7-3 Vectors in the Plane7-4 Polar Coordinates and Graphs7-5 Complex Numbers and De Moivre's TheoremChapter 7 ReviewChapter 7 Group Activity: Conic Sections and Planetary OrbitsCumulative Review Exercise for Chapters 5, 6, and 7CHAPTER 8 MODELING WITH SYSTEMS OF EQUATIONS AND INEQUALITIES8-1 Systems of Linear Equations in Two Variables8-2 Systems of Linear Equations in Three Variables8-3 Systems of Linear Inequalities8-4 Linear ProgrammingChapter 8 ReviewChapter 8 Group Activity: Modeling with Systems of EquationsCHAPTER 9 MATRICES AND DETERMINANTS9-1 Matrix Solutions to Linear Systems9-2 Matrix Operations9-3 Inverse of a Square Matrix9-4 Matrix Equations and Systems of Linear Equations9-5 Determinants9-6 Properties of Determinants9-7 Determinants and Cramer's RuleChapter 9 ReviewChapter 9 Group Activity: Using Matrices to Find Cost, Revenue, and ProfitCumulative Review Exercise for Chapters 8 and 9CHAPTER 10 SEQUENCES, INDUCTION, PROBABILITY10-1 Sequences and Series10-2 Mathematical Induction10-3 Arithmetic and Geometric Sequences10-4 Multiplication Principle, Permutations, and Combinations10-5 Sample Spaces and Probability10-6 Binomial FormulaChapter 10 ReviewChapter 10 Group Activity: Sequences Specified by Recursion FormulasCHAPTER 11 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY11-1 Conic Sections; Parabola11-2 Ellipse11-3 Hyperbola11-4 Translation and Rotation of Axes11-5 Systems of Nonlinear EquationsChapter 11 ReviewChapter 11 Group Activity: Focal ChordsCumulative Review Exercise for Chapters 10 and 11Appendix A BASIC ALGEBRA REVIEWA-1 Algebra and Real NumbersA-2 ExponentsA-3 RadicalsA-4 Polynomials: Basic OperationsA-5 Polynomials: FactoringA-6 Rational Expressions: Basic OperationsAppendix A ReviewAppendix A Group Activity: Rational Number RepresentationsAppendix B REVIEW OF EQUATIONS AND GRAPHINGB-1 Linear Equations and InequalitiesB-2 Cartesian Coordinate SystemB-3 Basic Formulas in Analytic GeometryAppendix C SPECIAL TOPICSC-1 Significant DigitsC-2 Partial FractionsC-3 Parametric EquationsAppendix D GEOMETRIC FORMULAS

Über Autor(innen)

Sobecki, David
I was born and raised in Cleveland, and started college at Bowling Green State University in 1984 majoring in creative writing. Eleven years later, I walked across the graduation stage to receive a PhD in math, a strange journey indeed. After two years at Franklin and Marshall College in Pennsylvania, I came home to Ohio, accepting a tenure-track job at the Hamilton campus of Miami University. Ive won a number of teaching awards in my career, and while maintaining an active teaching schedule, I now spend an inordinate amount of time writing textbooks and course materials. Ive written or co-authored either seven or twelve textbooks, depending on how you count them, as well as several solutions manuals and interactive CD-ROMS. After many years as developmental math coordinator at Miami Hamilton, I share the frustration that goes along with low pass rates in the developmental math curriculum. Far too many students end up on the classic Jetsons-style treadmill, with the abstract nature of the traditional algebra curriculum keeping them from reaching their goals. Like so many instructors across the country, I believe the time is right to move beyond the one-size-fits-all curriculum that treats students the same whether they hope to be an engineer or a pastry chef. Because weve always done it that way is NOT a good reason to maintain the status quo in our curriculum. Lets work together to devise alternate pathways that help students to learn more and learn better while hastening their trip into credit-bearing math courses. Since my book (Math in Our World) is written for the Liberal Arts Math and Quantitative Literacy market, I think Im in the right place at the right time to make a difference in the new and exciting pathways course. Im in a very happy place right now: my love of teaching meshes perfectly with my childhood dream of writing. (Dont tell my publisher this they think I spend 20 hours a day working on textbooks but Im working on my first novel in the limited spare time that I have.) Im also a former coordinator of Ohio Project NExT, as I believe very strongly in helping young college instructors focus on high-quality teaching as a primary career goal. I live in Fairfield, Ohio with my lovely wife Cat and fuzzy dogs Macleod and Tessa. When not teaching or writing, my passions include Ohio State football, Cleveland Indians baseball, heavy metal music, travel, golf, and home improvement.