College algebra with trigonometry : graphs and models

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Aims to encourage students to investigate mathematical ideas and processes graphically, numerically, and algebraically. This title focuses on the development of a library of elementary functions, including their important properties and uses. Many applications are real-world problems taken from professional journals and professional books.

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 Zeros 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 and Models

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 Review of Equations and Graphing

A.1 Linear Equations and Inequalities

A.2 Cartesian Coordinate System

A.3 Basic Formulas in Analytic Geometry

Appendix B Special Topics

B.1 Significant Digits

B.2 Partial Fractions

B.3 Descartes' Rule of Signs

B.4 Parametric Equations

Appendix C Geometric Formulas

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Summary

Summary

Table of Contents