Synopses & Reviews
The Fourth Edition of College Algebra continues to promote student success by engaging students in mathematics, thus helping them see the dynamic link between concepts and applications. The authors' hallmark approach, the Aufmann Interactive Method, encourages students to interact with math by presenting an annotated example, then guiding students with a Try Exercise, and finally presenting a worked-out solution for immediate reinforcement of the concept. A wealth of new features designed to enhance learning include more in-text guidance as well as special web-based resources, and an unparalleled Instructor's Annotated Edition facilitates teaching.New! An Instructor's Annotated Edition, unlike any other offered for this course, features reduced student text pages with special instructor resources in the margins: teaching tips, extra examples, ideas for reinforcing concepts, discussion suggestions, highlighted vocabulary and symbols, challenge problems, quizzes, suggested assignments, and references to transparencies that may be found both in the Instructor's Resource Manual and on the web site.New! Side-by-Side Solutions to examples pair an algebraic solution and a graphical representation to accommodate different learning styles.New! Technology-dependent modeling sections introduce the idea of mathematical modeling of data through linear, quadratic, exponential, logarithmic, and logistic regression.New! Integrated web resources include selected Take Note boxes (identified by a special web icon) which direct students to an interactive example or a downloadable file on the web site. These special resources can be used by instructors for presentation purposes or can be assigned tostudents to help them 'visualize' a concept.New! Concept Lists now prominently feature all the major topics at the beginning of each section, preparing students for the concepts to follow.A wide range of applications, exercise sets, and supplemental exercises--many involving real data--encourage problem solving, skill building, group work, writing, and manipulation of graphing calculators.Exploring Concepts with Technology, a special end-of-chapter feature, expands on ideas introduced in the text by using technology to investigate extended mathematical applications or topics.Projects at the end of each exercise set are designed to encourage students (or groups of students) to research and write about mathematics and its applications. Additional Projects are included in the Instructor's Resource Manual and on the book's web site.Topics for Discussion, conceptual exercises included at the end of each section, can be used for discussion or writing assignments.Take Note and Math Matters (formerly called Point of Interest) margin notes alert students about interesting aspects of math history, applications, and points that require special attention.
Synopsis
This text provides a supportive environment to help students successfully learn the content of a standard algebra course. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, focus their studying habits, and obtain greater mathematical success.
Table of Contents
Note: Each chapter concludes with a Summary, True/False Exercises, Review Exercises, and a Test. Chapters 1-8 include Cumulative Review Exercises. P. Preliminary Concepts Section P.1 The Real Number System Section P.2 Integer and Rational Number Exponents Section P.3 Polynomials Section P.4 Factoring Section P.5 Rational Expressions Section P.6 Complex Numbers Exploring Concepts with Technology: Can You Trust Your Calculator? 1. Equations and Inequalities Section 1.1 Linear and Absolute Value Equations Section 1.2 Formulas and Applications Section 1.3 Quadratic Equations Section 1.4 Other Types of Equations Section 1.5 Inequalities Section 1.6 Variation and Applications Exploring Concepts with Technology: Use a Graphing Calculator to Solve Equations 2. Functions and Graphs Section 2.1 A Two-Dimensional Coordinate System and Graphs Section 2.2 Introduction to Functions Section 2.3 Linear Functions Section 2.4 Quadratic Functions Section 2.5 Properties of Graphs Section 2.6 The Algebra of Functions Section 2.7 Modeling Data Using Regression Exploring Concepts with Technology: Graphing Piecewise Functions with a Graphing Calculator 3. Polynomial and Rational Functions Section 3.1 The Remainder Theorem and the Factor Theorem Section 3.2 Polynomial Functions of Higher Degree Section 3.3 Zeros of Polynomial Functions Section 3.4 The Fundamental Theorem of Algebra Section 3.5 Graphs of Rational Functions and Their Applications Exploring Concepts with Technology: Finding Zeros of a Polynomial Using Mathematica 4. Exponential and Logarithmic Functions Section 4.1 Inverse Functions Section 4.2 Exponential Functions and Their Applications Section 4.3 Logarithmic Functions and Their Applications Section 4.4 Logarithms and Logarithmic Scales Section 4.5 Exponential and Logarithmic Equations Section 4.6 Exponential Growth and Decay Section 4.7 Modeling Data with Exponential and Logarithmic Functions Exploring Concepts with Technology: Using a Semilog Graph to Model Exponential Decay 5. Topics in Analytic Geometry Section 5.1 Parabolas Section 5.2 Ellipses Section 5.3 Hyperbolas Exploring Concepts with Technology: Using a Graphing Calculator to Illustrate a Property of Parabolas 6. Systems of Equations Section 6.1 Systems of Linear Equations in Two Variables Section 6.2 Systems of Linear Equations in More Than Two Variables Section 6.3 Nonlinear Systems of Equations Section 6.4 Partial Fractions Section 6.5 Inequalities in Two Variables and Systems of Inequalities Section 6.6 Linear Programming Exploring Concepts with Technology: Ill-Conditioned Systems of Equations 7. Matrices Section 7.1 Gaussian Elimination Method Section 7.2 The Algebra of Matrices Section 7.3 The Inverse of a Matrix Section 7.4 Determinants Section 7.5 Cramer's Rule Exploring Concepts with Technology: Stochastic Matrices 8. Sequences, Series, and Probability Section 8.1 Infinite Sequences and Summation Notation Section 8.2 Arithmetic Sequences and Series Section 8.3 Geometric Sequences and Series Section 8.4 Mathematical Induction Section 8.5 The Binomial Theorem Section 8.6 Permutations and Combinations Section 8.7 Introduction to Probability Exploring Concepts with Technology: Mathematical Expectation Solutions to the Try Exercises Answers to Selected Exercises Index