Precalculus, 7th edition

  • John Hornsby, 
  • Margaret L. Lial, 
  • Gary K. Rockswold

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Precalculus helps you develop the balance of conceptual understanding and analytical skills needed to succeed in mathematics.

Published by Pearson (September 1st 2020) - Copyright © 2021

ISBN-13: 9780136881100

Subject: Precalculus, College Algebra & Trigonometry

Category: Precalculus

Table of contents

Table of Contents

  1. Review of Basic Concepts
    • R-1 Fractions, Decimals, and Percents
    • R-2 Sets and Real Numbers
    • R-3 Real Number Operations and Properties
    • R-4 Integer and Rational Exponents
    • R-5 Polynomials
    • R-6 Factoring Polynomials
    • R-7 Rational Expressions
    • R-8 Radical Expressions
  1. Equations and Inequalities
    • 1-1 Linear Equations
    • 1-2 Applications and Modeling with Linear Equations
    • 1-3 Complex Numbers
    • 1-4 Quadratic Equations
    • 1-5 Applications and Modeling with Quadratic Equations
    • 1-6 Other Types of Equations and Applications
    • 1-7 Inequalities
    • 1-8 Absolute Value Equations and Inequalities
  2. Graphs and Functions
    • 2-1 Rectangular Coordinates and Graphs
    • 2-2 Circles
    • 2-3 Functions
    • 2-4 Linear Functions
    • 2-5 Equations of Lines and Linear Models
    • 2-6 Graphs of Basic Functions
    • 2-7 Graphing Techniques
    • 2-8 Function Operations and Composition
  3. Polynomial and Rational Functions
    • 3-1 Quadratic Functions and Models
    • 3-2 Synthetic Division
    • 3-3 Zeros of Polynomial Functions
    • 3-4 Polynomial Functions: Graphs, Applications, and Models
    • 3-5 Rational Functions: Graphs, Applications, and Models
    • 3-6 Polynomial and Rational Inequalities
    • 3-7 Variation
  4. Inverse, Exponential, and Logarithmic Functions
    • 4-1 Inverse Functions
    • 4-2 Exponential Functions
    • 4-3 Logarithmic Functions
    • 4-4 Evaluating Logarithms and the Change-of-Base Theorem
    • 4-5 Exponential and Logarithmic Equations
    • 4-6 Applications of Models of Exponential Growth and Decay
  5. Trigonometric Functions
    • 5-1 Angles
    • 5-2 Trigonometric Functions
    • 5-3 Trigonometric Function Values and Angle Measures
    • 5-4 Solutions and Applications of Right Triangles
  6. The Circular Functions and Their Graphs
    • 6-1 Radian Measure
    • 6-2 The Unit Circle and Circular Functions
    • 6-3 Graphs of the Sine and Cosine Functions
    • 6-4 Translations of the Graphs of the Sine and Cosine Functions
    • 6-5 Graphs of the Tangent and Cotangent Functions
    • 6-6 Graphs of the Secant and Cosecant Functions
    • 6-7 Harmonic Motion
  7. Trigonometric Identities and Equations
    • 7-1 Fundamental Identities
    • 7-2 Verifying Trigonometric Identities
    • 7-3 Sum and Difference Identities
    • 7-4 Double-Angle and Half-Angle Identities
    • 7-5 Inverse Circular Functions
    • 7-6 Trigonometric Equations
    • 7-7 Equations Involving Inverse Trigonometric Functions
  8. Applications of Trigonometry
    • 8-1 The Law of Sines
    • 8-2 The Law of Cosines
    • 8-3 Geometrically Defined Vectors and Applications
    • 8-4 Algebraically Defined Vectors and the Dot Product
    • 8-5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients
    • 8-6 De Moivre’s Theorem; Powers and Roots of Complex Numbers
    • 8-7 Polar Equations and Graphs
    • 8-8 Parametric Equations, Graphs, and Applications
  9. Systems and Matrices
    • 9-1 Systems of Linear Equations
    • 9-2 Matrix Solution of Linear Systems
    • 9-3 Determinant Solution of Linear Systems
    • 9-4 Partial Fractions
    • 9-5 Nonlinear Systems of Equations
    • 9-6 Systems of Inequalities and Linear Programming
    • 9-7 Properties of Matrices
    • 9-8 Matrix Inverses
  10. Analytic Geometry
    • 10-1 Parabolas
    • 10-2 Ellipses
    • 10-3 Hyperbolas
    • 10-4 Summary of the Conic Sections
  11. Further Topics in Algebra
    • 11-1 Sequences and Series
    • 11-2 Arithmetic Sequences and Series
    • 11-3 Geometric Sequences and Series
    • 11-4 The Binomial Theorem
    • 11-5 Mathematical Induction
    • 11-6 Basics of Counting Theory
    • 11-7 Basics of Probability

Appendix A Polar Form of Conic Sections

Appendix B Rotation of Axes

Appendix C Geometry Formulas

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