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Precalculus

by Paul Sisson

Precalculus begins with a comprehensive study of functions and their applications and then continues with more advanced material, all designed to prepare students for calculus. A full review of college algebra topics is integrated with a rigorous presentation of concepts that form the foundation of calculus, including a detailed coverage of trigonometry. Each chapter provides historical context, technology notes, and applications.

Updates to the third edition include a more streamlined table of contents, new chapters (Chapter 4: Working with Functions and Chapter 13: An Introduction to Limits, Continuity, and the Derivative), and more robust content.

New topics covered include:

  • The difference quotient

  • Constructing mathematical models

  • Regression (linear, quadratic, exponential, logistic, and logarithmic)

  • Interpolation and extrapolation

  • Intervals of monotonicity

  • Local extrema

  • Average rate of change

  • Stretching and compressing graphs horizontally

  • Solving elementary logarithmic equations

  • The Pythagorean Theorem

  • The Unit Circle

  • Simple Harmonic Motion

  • Hyperbolic Functions

  • Systems of linear inequalities

  • Systems of nonlinear inequalities


Formats: Software, Textbook, Guided Notebook, eBook

Product ISBN
Software + eBook 978-1-642771-74-9
Software + eBook + Textbook 978-1-64277-284-5
Software + eBook + Guided Notebook 978-1-64277-345-3

Table of Contents

  1. Chapter 1: Algebraic Expressions, Equations, and Inequalities
    1. 1.1 Real Numbers and Algebraic Expressions
    2. 1.2 Properties of Exponents and Radicals
    3. 1.3 Polynomials and Factoring
    4. 1.4 Rational Expressions
    5. 1.5 Complex Numbers
    6. 1.6 Linear Equations in One Variable
    7. 1.7 Linear Inequalities in One Variable
    8. 1.8 Polynomial and Polynomial-Like Equations in One Variable
    9. 1.9 Rational and Radical Equations in One Variable
    10. Chapter 1 Review
  2. Chapter 2: Equations and Inequalities in Two Variables
    1. 2.1 The Cartesian Coordinate System
    2. 2.2 Circles
    3. 2.3 Linear Equations in Two Variables
    4. 2.4 Slope and Forms of Linear Equations
    5. 2.5 Parallel and Perpendicular Lines
    6. 2.6 Linear Inequalities in Two Variables
    7. Chapter 2 Review
  3. Chapter 3: Relations, Functions, and Their Graphs
    1. 3.1 Relations and Functions
    2. 3.2 Linear Functions
    3. 3.3 Quadratic Functions
    4. 3.4 Other Common Functions
    5. 3.5 Variation and Multivariable Functions
    6. 3.6 Mathematical Models
    7. Chapter 3 Review
  4. Chapter 4: Working with Functions
    1. 4.1 Transformations of Functions
    2. 4.2 Properties of Functions
    3. 4.3 Combining Functions
    4. 4.4 Inverses of Functions
    5. Chapter 4 Review
  5. Chapter 5: Polynomial and Rational Functions
    1. 5.1 Polynomial Functions and Polynomial Inequalities
    2. 5.2 Polynomial Division and the Division Algorithm
    3. 5.3 Locating Real Zeros of Polynomial Functions
    4. 5.4 The Fundamental Theorem of Algebra
    5. 5.5 Rational Functions and Rational Inequalities
    6. Chapter 5 Review
  6. Chapter 6: Exponential and Logarithmic Functions
    1. 6.1 Exponential Functions and Their Graphs
    2. 6.2 Exponential Models
    3. 6.3 Logarithmic Functions and Their Graphs
    4. 6.4 Logarithmic Properties and Models
    5. 6.5 Exponential and Logarithmic Equations
    6. Chapter 6 Review
  7. Chapter 7: Trigonometric Functions
    1. 7.1 Radian and Degree Measure
    2. 7.2 Trigonometric Functions and Right Triangles
    3. 7.3 Trigonometric Functions and the Unit Circle
    4. 7.4 Graphs of Sine and Cosine Functions
    5. 7.5 Graphs of Other Trigonometric Functions
    6. 7.6 Inverse Trigonometric Functions
    7. Chapter 7 Review
  8. Chapter 8: Trigonometric Identities and Equations
    1. 8.1 Fundamental Trigonometric Identities
    2. 8.2 Sum and Difference Identities
    3. 8.3 Product-Sum Identities
    4. 8.4 Trigonometric Equations
    5. Chapter 8 Review
  9. Chapter 9: Additional Topics in Trigonometry
    1. 9.1 The Law of Sines
    2. 9.2 The Law of Cosines
    3. 9.3 Polar Coordinates and Polar Equations
    4. 9.4 Parametric Equations
    5. 9.5 Trigonometric Form of Complex Numbers
    6. 9.6 Vectors in the Cartesian Plane
    7. 9.7 The Dot Product
    8. 9.8 Hyperbolic Functions
    9. Chapter 9 Review
  10. Chapter 10: Conic Sections
    1. 10.1 Ellipses
    2. 10.2 Parabolas
    3. 10.3 Hyperbolas
    4. 10.4 Rotation of Conic Sections
    5. 10.5 Polar Equations of Conic Sections
    6. Chapter 10 Review
  11. Chapter 11: Systems of Equations and Inequalities
    1. 11.1 Solving Systems of Linear Equations by Substitution and Elimination
    2. 11.2 Matrix Notation and Gauss-Jordan Elimination
    3. 11.3 Determinants and Cramer's Rule
    4. 11.4 Basic Matrix Operations
    5. 11.5 Inverses of Matrices
    6. 11.6 Partial Fraction Decomposition
    7. 11.7 Systems of Linear Inequalities and Linear Programming
    8. 11.8 Systems of Nonlinear Equations and Inequalities
    9. Chapter 11 Review
  12. Chapter 12: Sequences, Series, Combinatorics, and Probability
    1. 12.1 Sequences and Series
    2. 12.2 Arithmetic Sequences and Series
    3. 12.3 Geometric Sequences and Series
    4. 12.4 Mathematical Induction
    5. 12.5 Combinatorics
    6. 12.6 Probability
    7. Chapter 12 Review
  13. Chapter 13: An Introduction to Limits, Continuity, and the Derivative
    1. 13.1 Rates of Change and Tangents
    2. 13.2 Limits in the Plane
    3. 13.3 The Mathematical Definition of Limit
    4. 13.4 Determining Limits of Functions
    5. 13.5 Continuity
    6. 13.6 The Derivative
    7. Chapter 13 Review