College Algebra and Trigonometry

J.S. Ratti has been teaching mathematics at all levels for over 35 years. He is currently a full professor of mathematics and director of the Center for Mathematical Services at the University of South Florida. Professor Ratti is the author of numerous research papers in analysis, graph theory, and probability. He has won several awards for excellence in undergraduate teaching at University of South Florida and is the coauthor of a successful finite mathematics textbook.   Marcus McWaters is currently the chair of the Mathematics Department at the University of South Florida, a position he has held for the last eleven years. Since receiving his PhD in mathematics from the University of Florida, he has taught all levels of undergraduate and graduate courses, with class sizes ranging from 3 to 250. As chair, he has worked intensively to structure a course delivery system for lower level courses that would improve the low retention rate these courses experience across the country. When not involved with mathematics or administrative activity, he enjoys playing racquetball, spending time with his two daughters, and traveling the world with his wife.

P. Basic Concepts of Algebra

P.1 The Real Numbers and Their Properties

P.2 Integer Exponents and Scientific Notation

P.3 Polynomials

P.4 Factoring Polynomials

P.5 Rational Expressions

P.6 Rational Exponents and Radicals

            Chapter P Summary

            Chapter P Review Exercises

            Chapter P Practice Test A

            Chapter P Practice Test B

 

1. Equations and Inequalities

1.1 Linear Equations in One Variable

1.2 Quadratic Equations

1.3 Complex Numbers: Quadratic Equations with Complex Solutions

1.4 Solving Other Types of Equations

1.5 Inequalities

1.6 Equations and Inequalities Involving Absolute Value

            Chapter 1 Summary

            Chapter 1 Review Exercises

            Chapter 1 Practice Test A

            Chapter 1 Practice Test B

 

2. Graphs and Functions

2.1 The Coordinate Plane

2.2 Graphs of Equations

2.3 Lines

2.4 Functions

2.5 Properties of Functions

2.6 A Library of Functions

2.7 Transformations of Functions

2.8 Combining Functions; Composite Functions

2.9 Inverse Functions

            Chapter 2 Summary

            Chapter 2 Review Exercises

            Chapter 2 Practice Test A

            Chapter 2 Practice Test B

            Cumulative Review Exercises- Chapters P-2

 

3. Polynomial and Rational Functions

3.1 Quadratic Functions

3.2 Polynomial Functions

3.3 Dividing Polynomials

3.4 The Real Zeros of a Polynomial Function

3.5 The Complex Zeros of a Polynomial Function

3.6 Rational Functions

3.7 Variation

            Chapter 3 Summary

            Chapter 3 Review Exercises

            Chapter 3 Practice Test A

            Chapter 3 Practice Test B

            Cumulative Review Exercises- Chapters P-3

 

4. Exponential and Logarithmic Functions

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Rules of Logarithms

4.4 Exponential and Logarithmic Equations and Inequalities

4.5 Logarithmic Scales

            Chapter 4 Summary

            Chapter 4 Review Exercises

            Chapter 4 Practice Test A

            Chapter 4 Practice Test B

            Cumulative Review Exercises- Chapters P-4

 

5. Trigonometric Functions

5.1 Angles and Their Measure

5.2 Right-Triangle Trigonometry

5.3 Trigonometric Functions of Any Angle; The Unit Circle

5.4 Graphs of the Sine and Cosine Functions

5.5 Graphs of the Other Trigonometric Functions

5.6 Inverse Trigonometric Functions

            Chapter 5 Summary

            Chapter 5 Review Exercises

            Chapter 5 Practice Test A

            Chapter 5 Practice Test B

            Cumulative Review Exercises- Chapters P-5

 

6. Trigonometric Identities and Equations

6.1 Verifying Identities

6.2 Sum and Difference Formulas

6.3 Double-Angle and Half-Angle Formulas

6.4 Product-to-Sum and Sum-to-Product Formulas

6.5 Trigonometric Equations I

6.6 Trigonometric Equations II

            Chapter 6 Summary

            Chapter 6 Review Exercises

            Chapter 6 Practice Test A

            Chapter 6 Practice Test B

            Cumulative Review Exercises- Chapters P-6

 

7. Applications of Trigonometric Functions

7.1 The Law of Sines

7.2 The Law of Cosines

7.3 Areas of Polygons Using Trigonometry

7.4 Vectors

7.5 The Dot Product

7.6 Polar Coordinates

7.7 Polar Form of Complex Numbers; DeMoivre’s Theorem

            Chapter 7 Summary

            Chapter 7 Review Exercises

            Chapter 7 Practice Test A

            Chapter 7 Practice Test B

            Cumulative Review Exercises- Chapters P-7

 

8. Systems of Equations and Inequalities

8.1 Systems of Linear Equations in Two Variables

8.2 Systems of Linear Equations in Three Variables

8.3 Partial-Fraction Decomposition

8.4 Systems of Nonlinear Equations

8.5 Systems of Inequalities

8.6 Linear Programming

            Chapter 8 Summary

            Chapter 8 Review Exercises

            Chapter 8 Practice Test A

            Chapter 8 Practice Test B

            Cumulative Review Exercises- Chapters P-8

 

9. Matrices and Determinants

9.1 Matrices and Systems of Equations

9.2 Matrix Algebra

9.3 The Matrix Inverse

9.4 Determinants and Cramer’s Rule

            Chapter 9 Summary

            Chapter 9 Review Exercises

            Chapter 9 Practice Test A

            Chapter 9 Practice Test B

            Cumulative Review Exercises- Chapters P-9

 

10. Conic Sections

10.1 Conic Sections: Overview

10.2 The Parabola

10.3 The Ellipse

10.4 The Hyperbola

            Chapter 10 Summary

            Chapter 10 Review Exercises

            Chapter 10 Practice Test A

            Chapter 10 Practice Test B

            Cumulative Review Exercises- Chapters P-10

 

11. Further Topics in Algebra

11.1 Sequences and Series

11.2 Arithmetic Sequences; Partial Sums

11.3 Geometric Sequences and Series

11.4 Mathematical Induction

11.5 The Binomial Theorem

11.6 Counting Principles

11.7 Probability

            Chapter 11 Summary

            Chapter 11 Review Exercises

            Chapter 11 Practice Test A

            Chapter 11 Practice Test B

            Cumulative Review Exercises- Chapters P-11