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Table of Contents
1. Graphs
1.1 The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations
1.2 Intercepts; Symmetry; Graphing Key Equations
1.3 Solving Equations Using a Graphing Utility
1.4 Lines
1.5 Circles
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
2. 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 Review
Chapter Test
Cumulative Review
Chapter Projects
3. Linear and Quadratic Functions
3.1 Linear Functions, Their Properties, and Linear Models
3.2 Building Linear Models from Data
3.3 Quadratic Functions and Their Properties
3.4 Building Quadratic Models from Verbal Descriptions and Data
3.5 Inequalities Involving Quadratic Functions
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
4. Polynomial and Rational Functions
4.1 Polynomial Functions and Models
4.2 The Real Zeros of a Polynomial Function
4.3 Properties of Rational Functions
4.4 The Graph of a Rational Function
4.5 Polynomial and Rational Inequalities
4.6 Complex Zeros; Fundamental Theorem of Algebra
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
5. 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 Review
Chapter Test
Cumulative Review
Chapter Projects
6. Trigonometric Functions
6.1 Angles and Their Measure
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; Building Sinusoidal Models
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
7. 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 Review
Chapter Test
Cumulative Review
Chapter Projects
8. 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 Review
Chapter Test
Cumulative Review
Chapter Projects
9. Polar Coordinates; Vectors
9.1 Polar Coordinates
9.2 Polar Equations and Graphs
9.3 The Complex Plane; DeMoivre's Theorem
9.4 Vectors
9.5 The Dot Product
9.6 Vectors in Space
9.7 The Cross Product
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
10. 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 Review
Chapter Test
Cumulative Review
Chapter Projects
11. 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 Review
Chapter Test
Cumulative Review
Chapter Projects
12. 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 Review
Chapter Test
Cumulative Review
Chapter Projects
13. Counting and Probability
13.1 Counting
13.2 Permutations and Combinations
13.3 Probability
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
14. 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 Review
Chapter Test
Cumulative Review
Chapter 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 Jobs
A.9 Interval Notation; Solving Inequalities
A.10 nth Roots; Rational Exponents
Appendix B. The Limit of a Sequence; Infinite Series
Answers
IndexCategory : Higher Education
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