Precalculus: A Unit Circle Approach / Edition 3

by J. S. Ratti, Marcus McWaters, Leslaw Skrzypek

Overview

For courses in Precalculus.

Providing the rigor of solid mathematics with an engaging and friendly approach

As teachers, Ratti and McWaters saw firsthand where their Precalculus and Calculus students struggled, where they needed help making connections, and what material they needed to be successful in calculus. They decided to partner and write this text with the primary goal of preparing students to be successful in calculus and future STEM courses. Their experience in the classroom shows in each chapter. The focus on conceptual development, real-life applications, and extensive exercises, encourages a deeper understanding of the mathematics. Precalculus: A Unit Circle Approach, 3rd Edition, includes thorough coverage of topics as preparation for calculus, including; trig identities, difference quotient, functional composition, decomposition and emphasizes graphing techniques/transformations.

Also available with MyLab Math

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Product Details

ISBN-13:	9780134433202
Publisher:	Pearson Education
Publication date:	02/02/2017
Edition description:	3rd ed.
Pages:	1104
Product dimensions:	8.40(w) x 11.00(h) x 1.40(d)

About the Author

J.S. Ratti (1935 - 2018) taught mathematics at all levels for over 35 years, most recently as a full professor and past chair of mathematics at the University of South Florida. Professor Ratti was the author of numerous research papers in analysis, graph theory and probability. He received several awards, including a USF Research Council Grant, USF Teaching Incentive Program (TIP) Award, USF Outstanding Undergraduate Teaching Award, and Academy of Applied Sciences grants; he was the coauthor of a successful finite mathematics textbook.

Marcus McWaters is currently an Associate Professor at the University of South Florida (USF). He is a former Chair of the Department of Mathematics and Statistics at USF. 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 successfully structured a course delivery system for lower-level courses that improved the low retention rate in those courses at USF. He is also a founding member of the USF Center for Digital and Computational Video. When not involved with mathematics or administrative activity, he enjoys traveling with his wife and two daughters, theater, waterskiing and racquetball.

Leslaw Skrzypek is currently the Chair of the Department of Mathematics and Statistics at the University of South Florida. His research is in the area of Banach Spaces and Approximation Theory. He is the recipient of a Fulbright Award and a NATO Advanced Grant research award, and is a founding director of the USF Center for Complex Data Systems. Throughout his career, Professor Skrzypek has enjoyed teaching all levels of courses, from remedial to graduate real analysis. Over the years he also has been involved in training students for the Mathematical Olympiads. He enjoys nature, listening to music and spending time with his family. 

Jessica Bernards has been teaching mathematics since 2005. She began her career at the high-school level and transitioned to teaching at Portland Community College in 2010. She has taught a wide range of mathematics courses from developmental math up to calculus and has created curricula for each level. Bernards is a member of AMATYC's Project ACCCESS Cohort 9, where she developed a math study skills program that is now used across the US. In 2017, she was the honored recipient of the Leila and Simon Peskoff AMATYC Award for her work with Project ACCCESS, and in 2021 received the AMATYC Teaching Excellence Award.

Wendy Fresh has been a full-time instructor at Portland Community College (PCC) since 1997. She has taught a wide range of classes, from developmental math through calculus, both on campus and online. Fresh began her teaching career in 1992 in both rural and urban high schools. Her love of creating curricula to bring classrooms to life has led to work with technologies that complement her many courses. She earned her bachelor's degree in mathematics education from the University of Oregon and her master's degree in the teaching of mathematics from Portland State University.

Table of Contents

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

2. Polynomial and Rational Functions

2.1 Quadratic Functions

2.2 Polynomial Functions

2.3 Dividing Polynomials and the Rational Zeros Test

2.4 Rational Functions

2.5 Polynomial and Rational Inequalities

2.6 Zeros of a Polynomial Function

2.7 Variation

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

3.5 Logarithmic Scales; Modeling

4. Trigonometric Functions

4.1 Angles and Their Measure

4.2 The Unit Circle; Trigonometric Functions of Real Numbers

4.3 Trigonometric Functions of Angles

4.4 Graphs of the Sine and Cosine Functions

4.5 Graphs of the Other Trigonometric Functions

4.6 Inverse Trigonometric Functions

5. Analytic Trigonometry

5.1 Trigonometric Identities

5.2 Sum and Difference Formulas

5.3 Double-Angle and Half-Angle Formulas

5.4 Product-to-Sum and Sum-to-Product Formulas

5.5 Trigonometric Equations

6. Applications of Trigonometric Functions

6.1 Right-Triangle Trigonometry

6.2 The Law of Sines

6.3 The Law of Cosines

6.4 Vectors

6.5 The Dot Product

6.6 Polar Coordinates

6.7 Polar Form of Complex Numbers; DeMoivre’s Theorem

7. Systems of Equations and Inequalities

7.1 Systems of Equations in Two Variables

7.2 Systems of Linear Equations in Three Variables

7.3 Systems of Inequalities

7.4 Matrices and Systems of Equations

7.5 Determinants and Cramer’s Rule

7.6 Partial-Fraction Decomposition

7.7 Matrix Algebra

7.8 The Matrix Inverse

8. Analytic Geometry

8.1 Conic Sections: Overview

8.2 The Parabola

8.3 The Ellipse

8.4 The Hyperbola

8.5 Rotation of Axes

8.6 Polar Equations of Conics

8.7 Parametric Equations

9. Further Topics in Algebra

9.1 Sequences and Series

9.2 Arithmetic Sequences; Partial Sums

9.3 Geometric Sequences and Series

9.4 Mathematical Induction

9.5 The Binomial Theorem

9.6 Counting Principles

9.7 Probability

10. An Introduction to Calculus

10.1 Finding Limits Using Tables and Graphs

10.2 Finding Limits Algebraically

10.3 Infinite Limits and Limits at Infinity

10.4 Introduction to Derivatives

10.5 Area and the Integral

Appendix A. Review

A.1 The Real Numbers; Integer Exponents

A.2 Polynomials

A.3 Rational Expressions

A.4 Radical and Rational Exponents

A.5 Topics in Geometry

A.6 Equations

A.7 Inequalities

A.8 Complex Numbers