Description
Book SynopsisMike Sullivan recently retired as Professor of Mathematics at Chicago State University, having taught there for more than 30 years. He received his PhD in mathematics from Illinois Institute of Technology. He is a native of Chicago's South Side and currently resides in Oak Lawn, Illinois. Mike has four children; the two oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. His son, Mike Sullivan, III, co-authored the Sullivan Graphing with Data Analysis series as well as this series. Mike has authored or co-authored more than ten books. He owns a travel agency, and splits his time between a condo in Naples, Florida and a home in Oak Lawn, where Mike enjoys gardening.
Mike Sullivan, III is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on
Table of Contents
Table of Contents
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Graphs
- 1.1 The Distance and Midpoint Formulas
- 1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
- 1.3 Lines
- 1.4 Circles
- Chapter 1 Review, Test, and Projects
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Functions and Their Graphs
- 2.1 Functions
- 2.2 The Graph of a Function
- 2.3 Properties of Functions
- 2.4 Library of Functions; Piecewise-defined Functions
- 2.5 Graphing Techniques: Transformations
- 2.6 Mathematical Models: Building Functions
- Chapter 2 Review, Test, and Projects
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Linear and Quadratic Functions
- 3.1 Properties of Linear Functions and Linear Models
- 3.2 Building Linear Models from Data
- 3.3 Quadratic Functions and Their Properties
- 3.4 Build Quadratic Models from Verbal Descriptions and from Data
- 3.5 Inequalities Involving Quadratic Functions
- Chapter 3 Review, Test, and Projects
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Polynomial and Rational Functions
- 4.1 Polynomial Functions
- 4.2 Graphing Polynomial Functions; Models
- 4.3 Properties of Rational Functions
- 4.4 The Graph of a Rational Function
- 4.5 Polynomial and Rational Inequalities
- 4.6 The Real Zeros of a Polynomial Function
- Chapter 4 Review, Test, and Projects
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Exponential and Logarithmic Functions
- 5.1 Composite Functions
- 5.2 One-to-One Functions; Inverse Functions
- 5.3 Exponential Functions
- 5.4 Logarithmic Functions
- 5.5 Properties of Logarithms
- 5.6 Logarithmic and Exponential Equations
- 5.7 Financial Models
- 5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
- 5.9 Building Exponential, Logarithmic, and Logistic Models from Data
- Chapter 5 Review, Test, and Projects
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Trigonometric Functions
- 6.1 Angles, Arc, Length, and Circular Motion
- 6.2 Trigonometric Functions: Unit Circle Approach
- 6.3 Properties of the Trigonometric Functions
- 6.4 Graphs of the Sine and Cosine Functions
- 6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
- 6.6 Phase Shift; Sinusoidal Curve Fitting
- Chapter 6 Review, Test, and Projects
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Analytic Trigonometry
- 7.1 The Inverse Sine, Cosine, and Tangent Functions
- 7.2 The Inverse Trigonometric Functions (Continued)
- 7.3 Trigonometric Equations
- 7.4 Trigonometric Identities
- 7.5 Sum and Difference Formulas
- 7.6 Double-angle and Half-angle Formulas
- 7.7 Product-to-Sum and Sum-to-Product Formulas
- Chapter 7 Review, Test, and Projects
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Applications of Trigonometric Functions
- 8.1 Right Triangle Trigonometry; Applications
- 8.2 The Law of Sines
- 8.3 The Law of Cosines
- 8.4 Area of a Triangle
- 8.5 Simple Harmonic Motion; Damped Motion; Combining Waves
- Chapter 8 Review, Test, and Projects
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Polar Coordinates; Vectors
- 9.1 Polar Coordinates
- 9.2 Polar Equations and Graphs
- 9.3 The Complex Plane; De Moivre’s Theorem
- 9.4 Vectors
- 9.5 The Dot Product
- 9.6 Vectors in Space
- 9.7 The Cross Product
- Chapter 9 Review, Test, and Projects
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Analytic Geometry
- 10.1 Conics
- 10.2 The Parabola
- 10.3 The Ellipse
- 10.4 The Hyperbola
- 10.5 Rotation of Axes; General Form of a Conic
- 10.6 Polar Equations of Conics
- 10.7 Plane Curves and Parametric Equations
- Chapter 10 Review, Test, and Projects
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Systems of Equations and Inequalities
- 11.1 Systems of Linear Equations: Substitution and Elimination
- 11.2 Systems of Linear Equations: Matrices
- 11.3 Systems of Linear Equations: Determinants
- 11.4 Matrix Algebra
- 11.5 Partial Fraction Decomposition
- 11.6 Systems of Nonlinear Equations
- 11.7 Systems of Inequalities
- 11.8 Linear Programming
- Chapter 11 Review, Test, and Projects
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Sequences; Induction; the Binomial Theorem
- 12.1 Sequences
- 12.2 Arithmetic Sequences
- 12.3 Geometric Sequences; Geometric Series
- 12.4 Mathematical Induction
- 12.5 The Binomial Theorem
- Chapter 12 Review, Test, and Projects
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Counting and Probability
- 13.1 Counting
- 13.2 Permutations and Combinations
- 13.3 Probability
- Chapter 13 Review, Test, and Projects
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A Preview of Calculus: The Limit, Derivative, and Integral of a Function
- 14.1 Finding Limits Using Tables and Graphs
- 14.2 Algebra Techniques for Finding Limits
- 14.3 One-sided Limits; Continuous Functions
- 14.4 The Tangent Problem; The Derivative
- 14.5 The Area Problem; The Integral
- Chapter 14 Review, Test, and Projects
Appendix A: Review
- A.1 Algebra Essentials
- A.2 Geometry Essentials
- A.3 Polynomials
- A.4 Synthetic Division
- A.5 Rational Expressions
- A.6 Solving Equations
- A.7 Complex Numbers; Quadratic Equations in the Complex Number System
- A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
- A.9 Interval Notation; Solving Inequalities
- A.10 nth Roots; Rational Exponents
Appendix B: Graphing Utilities
- B.1 The Viewing Rectangle
- B.2 Using a Graphing Utility to Graph Equations
- B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry
- B.4 Using a Graphing Utility to Solve Equations
- B.5 Square Screens
- B.6 Using a Graphing Utility to Graph Inequalities
- B.7 Using a Graphing Utility to Solve Systems of Linear Equations
- B.8 Using a Graphing Utility to Graph a Polar Equation
- B.9 Using a Graphing Utility to Graph Parametric Equations
Answers Credits Index
