Summary: Accessible to students and flexible for instructors, College Algebra and Trigonometry, Sixth Edition, uses the dynamic link between concepts and applications to bring mathematics to life. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, work independently, and obtain greater mathematical fluency. The text also includes technology features to accommodate courses that allow the option of using graphing calcul...show moreators. Additional program components that support student success include Eduspace tutorial practice, online homework, SMARTHINKING Live Online Tutoring, and Instructional DVDs.
The authors' proven Aufmann Interactive Method allows students to try a skill as it is presented in example form. This interaction between the examples and Try Exercises serves as a checkpoint to students as they read the textbook, do their homework, or study a section. In the Sixth Edition, Review Notes are featured more prominently throughout the text to help students recognize the key prerequisite skills needed to understand new concepts.
Updated! End-of-chapter exercises--Assessing Concepts--have been revised to include more question types including fill-in-the-blank, multiple choice, and matching.
Revised! Prepare for This Section exercises, formerly Prepare for the Next Section, have been moved from the end of each chapter to the beginning of each chapter and afford students the opportunity to test their understanding of prerequisite skills about to be covered.
New! Calculus Connection icons have been added to indicate topics that will be revisited in subsequent courses, laying the groundwork for further study.
New! A Quantitative Reasoning feature demonstrates math solutions to real-world problems and is compliant with MAA Guidelines and AMATYC 2006 Crossroads Revisited.
Applications require students to use problem-solving strategies and new skills to solve practical problems. Covering topics from many disciplines, including agriculture, business, chemistry, education, and sociology, these problems demonstrate to students the practicality and value of algebra.
Noted by a pie chart icon, Real Data examples and exercises require students to analyze and construct mathematical models from actual situations.
Appearing throughout the text, Integrating Technology notes offer relevant information about using graphing calculators as an alternative way to solve a problem. Step-by-step instructions allow students to use technology with confidence.
Exploring Concepts with Technology, an optional end-of-chapter feature, uses technology (graphing calculators, CAS, etc.) to explore ideas covered in the chapter. These investigations can be used in a variety of ways, such as group projects or extra-credit assignments. Together with Integrating Technology tips, this feature makes the text appropriate for courses that allow the use of graphing calculators.
P.1 The Real Number System P.2 Integer and Rational Number Exponents P.3 Polynomials P.4 Factoring P.5 Rational Expressions P.6 Complex Numbers
1. Equations and Inequalities
1.1 Linear and Absolute Value Equations 1.2 Formulas and Applications 1.3 Quadratic Equations 1.4 Other Types of Equations 1.5 Inequalities 1.6 Variation and Applications
2. Functions and Graphs
2.1 A Two Dimensional Coordinate System and Graphs 2.2 Introduction to Functions 2.3 Linear Functions 2.4 Quadratic Functions 2.5 Properties of Graphs 2.6 The Algebra of Functions 2.7 Modeling Data Using Regression
3. Polynomial and Rational Functions
3.1 The Remainder of Theorem and the Factor Theorem 3.2 Polynomial Functions of Higher Degree 3.3 Zeros of Polynomial Functions 3.4 The Fundamental Theorem of Algebra 3.5 Graphs of Rational Functions and Their Applications
4. Exponential and Logarithmic Functions
4.1 Inverse Functions 4.2 Exponential Functions and Their Applications 4.3 Logarithmic Functions and Their Applications 4.4 Properties of Logarithms and Logarithmic Scales 4.5 Exponential and Logarithmic Equations 4.6 Exponential Growth and Decay 4.7 Modeling Data with Exponential and Logarithmic Functions
5. Trigonometric Functions
5.1 Angles and Arcs 5.2 Trigonometric Functions of Acute Angles 5.3 Trigonometric Functions of Any Angle 5.4 Trigonometric Functions of Real Numbers 5.5 Graphs of the Sine and Cosine Functions 5.6 Graphs of the Other Trigonometric Functions 5.7 Graphing Techniques 5.8 Harmonic Motion--An Application of the Sine and Cosine Functions
6. Trigonometric Identities and Equations
6.1 Verification of Trigonometric Identities 6.2 Sum, Difference, and Cofunction Identities 6.3 Double- and Half-Angle Identities 6.4 Identities Involving the Sum of Trigonometric Functions 6.5 Inverse Trigonometric Functions 6.6 Trigonometric Equations
7. Applications of Trigonometry
7.1 The Law of Sines 7.2 The Law of Cosines and Area 7.3 Vectors 7.4 TrigonometricForm of Complex Numbers 7.5 De Moivre's Theorem
8. Topics in Analytic Geometry
8.1 Parabolas 8.2 Ellipses 8.3 Hyperbolas 8.4 Rotation of Axes 8.5 Introduction to Polar Coordinates 8.6 Polar Equations of the Conics 8.7 Parametric Equations
9. Systems of Equations and Inequalities
9.1 Systems of Linear Equations in Two Variables 9.2 Systems of Linear Equations in More than Two Variables 9.3 Nonlinear Systems of Equations 9.4 Partial Fractions 9.5 Inequalities in Two Variables and Systems of Inequalities 9.6 Linear Programming
10.1 Gaussian Elimination Method 10.2 The Algebra of Matrices 10.3 The Inverse of a Matrix 10.4 Determinants 10.5 Cramer's Rule
11. Sequences, Series, and Probability
11.1 Infinite Sequences and Summation Notation 11.2 Arithmetic Sequences and Series 11.3 Geometric Sequences and Series 11.4 Mathematical Induction 11.5 The Binomial Theorem 11.6 Permutations and Combinations 11.7 Introduction to Probability
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