College Algebra with Trigonometry : Graphs and Models

by Barnett, Raymond A.; Ziegler, Michael R.; Byleen, Karl E.

• ISBN13: 9780072916997
• ISBN10: 0072916990
• Edition: 1st
• Format: Hardcover
• Copyright: 2004-08-27
• Publisher: McGraw-Hill Science/Engineering/Math

Table of Contents

1 Functions, Graphs, and Models

1-1 Using Graphing Utilities

1-2 Functions

1-3 Functions: Graphs and Properties

1-4 Functions: Graphs and Transformations

1-5 Operations on Functions; Composition

1-6 Inverse Functions

2 Modeling with Linear and Quadratic Functions

2-1 Linear Functions

2-2 Linear Equations and Models

2-3 Quadratic Functions

2-4 Complex Numbers

2-5 Quadratic Equations and Models

2-6 Additional Equation-Solving Techniques

2-7 Solving Inequalities

3 Polynomial and Rational Functions

3-1 Polynomial Functions and Models

3-2 Real Zero and Polynomial Inequalities

3-3 Complex Zeros and Rational Zeros of Polynomials

3-4 Rational Functions and Inequalities

4 Exponential and Logarithmic Functions

4-1 Exponential Functions

4-2 Exponential Models

4-3 Logarithmic Functions

4-4 Logarithmic Models

4-5 Exponential and Logarithmic Equations

5 Trigonometric Functions

5-1 Angles and Their Measure

5-2 Right Triangle Trigonometry

5-3 Trigonometric Functions: A Unit Circle Approach

5-4 Properties of Trigonometric Functions

5-5 More General Trigonometric Functions

5-6 Inverse Trigonometric Functions

6 Trigonometric Identities and Conditional Equations

6-1 Basic Identities and Their Use

6-2 Sum, Difference, and Cofunction Identities

6-3 Double-Angle and Half-Angle Identities

6-4 Product-Sum and Sum-Product Identities

6-5 Trigonometric Equations

7 Additional Topics in Trigonometry

7-1 Law of Sines

7-2 Law of Cosines

7-3 Geometric Vectors

7-4 Algebraic Vectors

7-5 Polar Coordinates and Graphs

7-6 Complex Numbers in Rectangular and Polar Forms

7-7 De Moivre's Theorem

8 Modeling with Linear Systems

8-1 Systems of Linear Equations in Two Variables

8-2 Systems of Linear Equations and Augmented Matrices

8-3 Gauss-Jordan Elimination

8-4 Systems of Linear Inequalities

8-5 Linear Programming

9 Matrices and Determinants

9-1 Matrix Operations

9-2 Inverse of a Square Matrix

9-3 Matrix Equations and Systems of Linear Equations

9-4 Determinants

9-5 Properties of Determinants

9-6 Determinants and Cramer's Rule

10 Sequences, Induction, and Probability

10-1 Sequences and Series

10-2 Mathematical Induction

10-3 Arithmetic and Geometric Sequences

10-4 Multiplication Principle, Permutations, and Combinations

10-5 Sample Spaces and Probability

10-6 Binomial Formula

11 Additional Topics in Analytic Geometry

11-1 Conic Sections; Parabola

11-2 Ellipse

11-3 Hyperbola

11-4 Translation of Axes

11-5 Rotation of Axes

11-6 Nonlinear Systems

Appendix A Basic Algebra Review

Appendix B Special Topics

Appendix C Geometric Formulas