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Summary: This text provides a supportive environment to help students successfully learn the content of a standard algebra and trigonometry course. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, focus their studying habits, and obtain greater mathematical success.
Many new components added to this edition of College Algebra and Trigonometry have been designed to help students diagnose and review weak ...show morealgebra skills. Prerequisite review is include in the textbook (and supporting materials) so that instructors can spend less time covering review material and students can still fill in the gaps in their mathematical knowledge. ...show less
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 Semi-Log Graph to Model Exponential Decay
5. Trigonometric Functions
Section 5.1 Angles and Arcs
Section 5.2 Trigonometric Functions of Acute Angles
Section 5.3 Trigonometric Functions of Any Angle
Section 5.4 Trigonometric Functions of Real Numbers
Section 5.5 Graphs of the Sine and Cosine Functions
Section 5.6 Graphs of the Other Trigonometric Functions
Section 5.7 Graphing Techniques
Section 5.8 Harmonic Motion--An Application of the Sine and Cosine Functions
Exploring Concepts with Technology: Sinusoidal Families
6. Trigonometric Identities and Equations
Section 6.1 Verification of Trigonometric Identities
Section 6.2 Sum, Difference, and Cofunction Identities
Section 6.3 Double- and Half-Angle Identities
Section 6.4 Identities Involving the Sum of Trigonometric Functions
Section 6.5 Inverse Trigonometric Functions
Section 6.6 Trigonometric Equations
Exploring Concepts with Technology: Approximate an Inverse Trigonometric Function with Polynomials
7. Applications of Trigonometry
Section 7.1 The Law of Sines
Section 7.2 The Law of Cosines and Area
Section 7.3 Vectors
Section 7.4 Trigonometric Form of Complex Numbers
Section 7.5 De Moivre's Theorem
Exploring Concepts with Technology: Optimal Branching of Arteries
8. Topics in Analytic Geometry
Section 8.1 Parabolas
Section 8.2 Ellipses
Section 8.3 Hyperbolas
Section 8.4 Rotation of Axes
Section 8.5 Introduction to Polar Coordinates
Section 8.6 Polar Equations of the Conics
Section 8.7 Parametric Equations
Exploring Concepts with Technology: Using a Graphing Calculator to Find the nth Roots of z
9. Systems of Equations
Section 9.1 Systems of Linear Equations in Two Variables
Section 9.2 Systems of Linear Equations in More Than Two Variables
Section 9.3 Nonlinear Systems of Equations
Section 9.4 Partial Fractions
Section 9.5 Inequalities in Two Variables and Systems of Inequalities
Section 9.6 Linear Programming
Exploring Concepts with Technology: Ill-Conditioned Systems of
Section 10.1 Gaussian Elimination Method
Section 10.2 The Algebra of Matrices
Section 10.3 The Inverse of a Matrix
Section 10.4 Determinants
Section 10.5 Cramer's Rule
Exploring Concepts with Technology: Stochastic Matrices
11. Sequences, Series, and Probability
Section 11.1 Infinite Sequences and Summation Notation
Section 11.2 Arithmetic Sequences and Series
Section 11.3 Geometric Sequences and Series
Section 11.4 Mathematical Induction
Section 11.5 The Binomial Theorem
Section 11.6 Permutations and Combinations
Section 11.7 Introduction to Probability
Exploring Concepts with Technology: Mathematical Expectation
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