Algebra and Trigonometry

Michael Sullivan, Emeritus Professor of Mathematics at Chicago State University, received a Ph.D. in mathematics from the Illinois Institute of Technology. Mike taught at Chicago State for 35 years before recently retiring. He is a native of Chicago’s South Side and divides his time between a home in Oak Lawn IL and a condo in Naples FL.   Mike is a member of the American Mathematical Society and the Mathematical Association of America. He is a past president of the Text and Academic Authors Association and is currently Treasurer of its Foundation. He is a member of the TAA Council of Fellows and was awarded the TAA Mike Keedy award in 1997 and the Lifetime Achievement Award in 2007. In addition, he represents TAA on the Authors Coalition of America.   Mike has been writing textbooks for more than 35 years and currently has 15 books in print, twelve with Pearson Education. When not writing, he enjoys tennis, golf, gardening, and travel.   Mike has four children: Kathleen, who teaches college mathematics; Michael III, who also teaches college mathematics, and who is his coauthor on two precalculus series; Dan, who is a sales director for Pearson Education; and Colleen, who teaches middle-school and secondary school mathematics. Twelve grandchildren round out the family.

R. Review

R.1 Real Numbers

R.2 Algebra Essentials

R.3 Geometry Essentials

R.4 Polynomials

R.5 Factoring Polynomials

R.6 Synthetic Division

R.7 Rational Expressions

R.8 nth Roots; Rational Exponents

 

1. Equations and Inequalities

1.1 Linear Equations

1.2 Quadratic Equations

1.3 Complex Numbers; Quadratic Equations in the Complex Number System

1.4 Radical Equations; Equations Quadratic in Form;  Factorable Equations

1.5 Solving Inequalities

1.6 Equations and Inequalities Involving Absolute Value

1.7 Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Jobs Applications

 

2. Graphs

2.1 The Distance and Midpoint Formulas

2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry

2.3 Lines

2.4 Circles

2.5 Variation

 

3. Functions and Their Graphs

3.1 Functions

3.2 The Graph of a Function

3.3 Properties of Functions

3.4 Library of Functions; Piecewise-defined Functions

3.5 Graphing Techniques: Transformations

3.6 Mathematical Models: Building Functions

 

4. Linear and Quadratic Functions

4.1 Linear Functions and Their Properties

4.2 Linear Models: Building Linear Functions from Data

4.3 Quadratic Functions and Their Properties

4.4 Building Quadratic Models from Data

4.5 Inequalities Involving Quadratic Functions

 

5. Polynomial and Rational Functions

5.1 Polynomial Functions and Models

5.2 Properties of Rational Functions

5.3 The Graph of a Rational Function

5.4 Polynomial and Rational Inequalities

5.5 The Real Zeros of a Polynomial Function

5.6 Complex Zeros: Fundamental Theorem of Algebra

 

6. Exponential and Logarithmic Functions

6.1 Composite Functions

6.2 One-to-One Functions; Inverse Functions

6.3 Exponential Functions

6.4 Logarithmic Functions

6.5 Properties of Logarithms

6.6 Logarithmic and Exponential Equations

6.7 Financial Models

6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models

6.9 Building Exponential, Logarithmic, and Logistic Models from Data

 

7. Trigonometric Functions

7.1 Angles and Their Measure

7.2 Right Triangle Trigonometry

7.3 Computing the Values of Trigonometric Functions of Acute Angles

7.4 Trigonometric Functions of Any Angle

7.5 Unit Circle Approach; Properties of the Trigonometric Functions

7.6 Graphs of the Sine and Cosine Functions

7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions

7.8 Phase Shift; Sinusoidal Curve Fitting

 

8. Analytic Trigonometry

8.1 The Inverse Sine, Cosine, and Tangent Functions

8.2 The Inverse Trigonometric Functions (continued)

8.3 Trigonometric Equations

8.4 Trigonometric Identities

8.5 Sum and Difference Formulas

8.6 Double-Angle and Half-Angle Formulas

8.7 Product-to-Sum and Sum-to-Product Formulas

 

9. Applications of Trigonometric Functions

9.1 Applications Involving Right Triangles

9.2 Law of Sines

9.3 Law of Cosines

9.4 Area of a Triangle

9.5 Simple Harmonic Motion; Damped Motion; Combining Waves

 

10. Polar Coordinates; Vectors

10.1 Polar Coordinates

10.2 Polar Equations and Graphs

10.3 The Complex Plane; DeMoivre’s Theorem

10.4 Vectors

10.5 The Dot Product

 

11. Analytic Geometry

11.1 Conics

11.2 The Parabola

11.3 The Ellipse

11.4 The Hyperbola

11.5 Rotation of Axes; General Form of a Conic

11.6 Polar Equations of Conics

11.7 Plane Curves and Parametric Equations

 

12. Systems of Equations and Inequalities

12.1 Systems of Linear Equations: Substitution and Elimination

12.2 Systems of Linear Equations: Matrices

12.3 Systems of Linear Equations: Determinants

12.4 Matrix Algebra

12.5 Partial Fraction Decomposition

12.6 Systems of Nonlinear Equations

12.7 Systems of Inequalities

12.8 Linear Programming

 

13. Sequences; Induction; The Binomial Theorem

13.1 Sequences

13.2 Arithmetic Sequences

13.3 Geometric Sequences; Geometric Series

13.4 Mathematical Induction

13.5 The Binomial Theorem

 

14. Counting and Probability

14.1 Sets and Counting

14.2 Permutations and Combinations

14.3 Probability

 

Appendix: Graphing Utilities

1. The Viewing Rectangle

2. Using a Graphing Utility to Graph Equations

3. Using a Graphing Utility to Graph Equations Locating Intercepts and Checking for Symmetry

4. Using a Graphing Utility to Solve Equations

5. Square Screens

6. Using a Graphing Utility to Graph Inequalities

7. Using a Graphing Utility to Solve Systems of Linear Equations

8. Using a Graphing Utility to Graph a Polar Equation

9. Using a Graphing Utility to Graph Parametric Equations