Precalculus Essentials

Ratti and McWaters wrote this series with the primary goal of preparing students to be successful in calculus. Having taught both calculus and precalculus, the authors saw firsthand where students would struggle, where they needed help making connections, and what material they needed in order to succeed in calculus. Their experience in the classroom shows in each chapter, where they emphasize conceptual development, real-life applications, and extensive exercises to encourage a deeper understanding.

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 known as 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

P1 The Real Numbers; Integer Exponents

P2 Radicals and Rational Exponents

P3 Solving Equations

P4 Inequalities

P5 Complex Numbers

1. Graphs and Functions

1.1 Graphs of Equations

1.2 Lines

1.3 Functions

1.4 A Library of Functions

1.5 Transformations of Functions

1.6 Combining Functions; Composite Functions

1.7 Inverse Functions

            Chapter 1 Summary

            Chapter 1 Review Exercises

            Chapter 1 Practice Test A

            Chapter 1 Practice Test B

2. Polynomial and Rational Functions

2.1 Quadratic Functions

2.2 Polynomial Functions

2.3 Dividing Polynomials and the Rational Zeros Test

2.4 Zeros of a Polynomial Function

2.5 Rational Functions

            Chapter 2 Summary

            Chapter 2 Review Exercises

            Chapter 2 Practice Test A

            Chapter 2 Practice Test B

3. Exponential and Logarithmic Functions

3.1 Exponential Functions

3.2 Logarithmic Functions

3.3 Rules of Logarithms

3.4 Exponential and Logarithmic Equations and Inequalities

            Chapter 3 Summary

            Chapter 3 Review Exercises

            Chapter 3 Practice Test A

            Chapter 3 Practice Test B

4. Trigonometric Functions

4.1 Angles and Their Measure

4.2 The Unit Circle; Trigonometric Functions

4.3 Graphs of the Sine and Cosine Functions

4.4 Graphs of the Other Trigonometric Functions

4.5 Inverse Trigonometric Functions

4.6 Right-Triangle Trigonometry

4.7 Trigonometric Identities

4.8 Sum and Difference Formulas

            Chapter 4 Summary

            Chapter 4 Review Exercises

            Chapter 4 Practice Test A

            Chapter 4 Practice Test B

5. Applications of Trigonometric Functions

5.1 The Law of Sines and the Law of Cosines

5.2 Areas of Polygons Using Trigonometry

5.3 Polar Coordinates

5.4 Parametric Equations

            Chapter 5 Summary

            Chapter 5 Review Exercises

            Chapter 5 Practice Test A

            Chapter 5 Practice Test B

6. Further Topics in Algebra

6.1 Sequences and Series

6.2 Arithmetic Sequences; Partial Sums

6.3 Geometric Sequences and Series

6.4 Systems of Equations in Two Variables

6.5 Partial-Fraction Decomposition

            Chapter 6 Summary

            Chapter 6 Review Exercises

            Chapter 6 Practice Test A

            Chapter 6 Practice Test B

Appendix: Answers to Practice Problems

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