Precalculus, 7th edition

Published by Pearson (September 1, 2020) © 2021

  • John Hornsby University of New Orleans
  • Margaret L. Lial American River College

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ISBN-13: 9780136881100 (2020 update)
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Precalculus by Lial, Hornsby, Schneider and Daniels channels the experience of master teachers to help you develop the conceptual understanding and analytical skills you need to succeed in mathematics. A systematic approach is used to present each topic and is designed to actively engage you in the learning process. Ample opportunities for review are interspersed within chapters and also found at the end of chapters. The 7th Edition offers a complete suite of materials that supports all classroom types and learners. An expanded Chapter R includes more basic concepts that often challenge students, including a new section on Fractions, Decimals, and Percents.

R. 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

Appendices

  • A. Polar Form of Conic Sections
  • B. Rotation of Axes
  • C. Geometry Formulas

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