Precalculus

Auteur

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 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.

Texte du rabat

Normal 0 false false false 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. Precalculus: A Unit Circle Approach, Second Edition, offers the best of both worlds: rigorous topics and a friendly, "teacherly" tone.

Résumé
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. Precalculus: A Unit Circle Approach, Second Edition, offers the best of both worlds: rigorous topics and a friendly, “teacherly” tone.

Contenu

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

2.6 Variation

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Practice Test A

Chapter 2 Practice Test B

Cumulative Review Chapters 1–2

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

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Practice Test A

Chapter 3 Practice Test B

Cumulative Review Chapters 1–3

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

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Practice Test A

Chapter 4 Practice Test B

Cumulative Review Chapters 1–4

5. Analytic Trigonometry

5.1 Trigonometric Identities and Equations

5.2 Trigonometric Equations

5.3 Sum and Difference Formulas

5.4 Double-Angle and Half-Angle Formulas

5.5 Product-to-Sum and Sum-to-Product Formulas

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Practice Test A

Chapter 5 Practice Test B

Cumulative Review Chapters 1–5

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

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Practice Test A

Chapter 6 Practice Test B

Cumulative Review Chapters 1–6

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 Matrices and Systems of Equations

7.4 Determinants and Cramer's Rule

7.5 Partial–Fraction Decomposition

7.6 Matrix Algebra

7.7 The Matrix Inverse

7.8 Systems of Inequalities

Chapter 7 Summary

Chapter 7 Review Exercises

Chapter 7 Practice Test A

Chapter 7 Practice Test B

Cumulative Review Chapters 1–7

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

Chapter 8 Summary

Chapter 8 Review Exercises

Chapter 8 Practice Test A

Chapter 8 Practice Test B

Cumulative Review Chapters 1–8

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

Chapter 9 Summary

Chapter 9 Review Exercises

Chapter 9 Practice Test A

Chapter 9 Practice Test B

Cumulative Review Chapters 1–9

Appendix Review

A1. The Real Numbers; Integer Exponents

A2. Polynomials

A3. Rational Expressions

A4. Radicals and Rational Exponents

A5. Topics in Geometry

A6. Equations

A7. Inequalities

A8. Complex Numbers

Answers to Selected Exercises

Credits

Index of Applications

Index