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Precalculus: A Unit Circle Approach, 3rd edition

Published by Pearson (January 1, 2021) © 2018

  • J S Ratti University of South Florida
  • Marcus S. McWaters University of South Florida
  • Leslaw Skrzypek University Of South Florida
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Precalculus: A Unit Circle Approach provides the rigor of solid mathematics through an engaging and friendly approach. The authors focus on conceptual development, real-life applications and extensive exercises to encourage a deep understanding of the mathematics.

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

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