College Algebra With Trigonometry

by Barnett, Raymond; Ziegler, Michael; Byleen, Karl; Sobecki, David

• ISBN13: 9780077350109
• ISBN10: 0077350103
• Edition: 9th
• Format: Hardcover
• Copyright: 2010-01-19
• Publisher: McGraw-Hill Education

Summary

Barnett, Ziegler, Byleen, and Sobecki's College Algebra with Trigonometry text is designed to be user friendly and to maximize student comprehension by emphasizing computational skills, ideas, and problem solving as opposed to mathematical theory. The large number of pedagogical devices employed in this text will guide a student through the course. Integrated throughout the text, students and instructors will find Explore-Discuss boxes which encourage students to think critically about mathematical concepts. In each section, the worked examples are followed by matched problems that reinforce the concept being taught. In addition, the text contains an abundance of exercises and applications that will convince students that math is useful. A MathZone site featuring algorithmic exercises, videos, and other resources accompanies the text.

Table of Contents

Basic Algebraic Operations

Algebra and Real Numbers

Exponents and Radicals

Polynomials: Basic Operations and Factoring

Rational Expressions: Basic Operations

Review

Equations And Inequalities

Linear Equations and Applications

Linear Inequalities

Absolute Value

Complex Numbers

Quadratic Equations and Applications

Equations Involving Radicals

Chapter 1 Group Activity: Solving a Cubic Equation

Chapter 1 Review

Graphs

Rectangular Coordinates

Distance in the Plane

Equations of a Line

Linear Equations and Models

Chapter 2 Group Activity: Rates of Change

Chapter 2 Review

Functions

Functions

Graphing Functions

Transformations of Functions

Quadratic Functions

Combining Functions; Composition

Inverse Functions

Chapter 3 Group Activity: Mathematical Modeling - Choosing a Long-Distance Calling Plan

Chapter 3 Review

1, 2, & 3 Cumulative Review Exercises

Polynomial And Rational Functions

Polynomial Functions And Models

Real Zeros and Polynomial Inequalities

Complex Zeros and Rational Zeros of Polynomials

Rational Functions and Inequalities

Variation and Modeling

Chapter 4 Group Activity: Interpolating Polynomials

Chapter 4 Review

Exponential And Logarithmic Functions

Exponential Functions

Exponential Models

Logarithmic Functions

Logarithmic Models

Exponential and Logarithmic Equations

Chapter 5 Group Activity: Growth of Increasing Functions

Chapter 5 Review

4 & 5 Cumulative Review Exercises

Trigonometric Functions

Angles and Their Measure

Right Triangle Trigonometry

Trigonometric Functions: A Unit Circle Approach

Trigonometric Functions: Properties and Graphs

More General Trigonometric Functions

Inverse Trigonometric Functions

Chapter 6 Group Activity: A Predator-Prey Analysis Involving Mountain Lions and Deer

Chapter 6 Review

Trigonometric Identities And Conditional Equations

Basic Identities and Their Use

Sum, Difference, and Cofunction Identities

Double-Angle and Half-Angle Identities

Product-Sum and Sum-Product Identities

Trigonometric Equations

Chapter 7 Group Activity: From M sin Bt + N cos Bt to A sin(Bt + C) - A Harmonic Analysis Tool

Chapter 7 Review

Additional Topics In Trigonometry

Law of Sines

Law of Cosines

Vectors in the Plane

Polar Coordinates and Graphs

Complex Numbers and De Moivre's Theorem

Chapter 8 Group Activity: Conic Sections and Planetary Orbits

Chapter 8 Review

6, 7, & 8 Cumulative Review Exercises

Additional Topics In Analytic Geometry

Conic Sections; Parabola

Ellipse

Hyperbola

Rotation of Axes

Chapter 9 Group Activity: Focal Chords

Chapter 9 Review

Systems Of Equations And Inequalities; Matrices

Systems of Linear Equations

Solving Linear Systems Using Gauss-Jordan Elimination

Matrix Operations

Solving Linear Systems Using Inverse Matrices

Determinants and Cramer's Rule

Chapter 10 Group Activity: Modeling with Systems of Linear Equations

Systems of Nonlinear Equations

Systems of Linear Inequalities

Linear Programming

Chapter 10 Review

Sequences And Series

Sequences and Series

Mathematical Induction

Arithmetic and Geometric Sequences

Counting Techniques: Multiplication Principle, Permutations, and Combinations

Sample Spaces and Probability

Binomial Formula

Chapter 11 Group Activity: Sequences Specified by Recursion Formulas

Chapter 11 Review

9. 10, & 11 Cumulative Review Exercises

Limits: An Introduction To Calculus

Introduction to Limits

Computing Limits Algebraically

Limits at Infinity

The Derivative

Area and Calculus

Chapter 12 Group Activity: Derivatives of Exponential and Log Functions

Chapter 12 Review

Special Topics

Scientific Notation and Significant Digits

Partial Fractions

Parametric Equations

Geometric Formulas

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