Description
Michael Sullivan’s time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. The Enhanced with Graphing Utilities Serieshas evolved to meet today’s course needs by integrating the usage of graphing calculator, active-learning, and technology in new ways to help students be successful in their course, as well as in their future endeavors.
Table of Contents
R. Review
R.1 Real Numbers
R.2 Algebra Essentials
R.3 Geometry Essentials
R.4 Polynomials
R.5 Factoring Polynomials
R.6 Synthetic Division
R.7 Rational Expressions
R.8 nth Roots; Rational Exponents
1. Graphs, Equations, and Inequalities
1.1 The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations
1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations
1.3 Quadratic Equations
1.4 Complex Numbers; Quadratic Equations in the Complex Number System
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations; Factorable Equations
1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs
1.7 Solving Inequalities
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
2. Graphs
2.1 Intercepts; Symmetry; Graphing Key Equations
2.2 Lines
2.3 Circles
2.4 Variation
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
3. Functions and Their Graphs
3.1 Functions
3.2 The Graph of a Function
3.3 Properties of Functions
3.4 Library of Functions; Piecewise-defined Functions
3.5 Graphing Techniques: Transformations
3.6 Mathematical Models: Building Functions
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
4. Linear and Quadratic Functions
4.1 Linear Functions, Their Properties, and Linear Models
4.2 Building Linear Models from Data
4.3 Quadratic Functions and Their Properties
4.4 Building Quadratic Models from Verbal Descriptions and Data
4.5 Inequalities Involving Quadratic Functions
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
5. Polynomial and Rational Functions
5.1 Polynomial Functions and Models
5.2 The Real Zeros of a Polynomial Function
5.3 Properties of Rational Functions
5.4 The Graph of a Rational Function
5.5 Polynomial and Rational Inequalities
5.6 Complex Zeros; Fundamental Theorem of Algebra
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
6. Exponential and Logarithmic Functions
6.1 Composite Functions
6.2 One-to-One Functions; Inverse Functions
6.3 Exponential Functions
6.4 Logarithmic Functions
6.5 Properties of Logarithms
6.6 Logarithmic and Exponential Equations
6.7 Financial Models
6.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models
6.9 Building Exponential, Logarithmic, and Logistic Models from Data
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
7. Trigonometric Functions
7.1 Angles and Their Measure
7.2 Right Triangle Trigonometry
7.3 Computing the Values of Trigonometric Functions of Acute Angles
7.4 Trigonometric Functions of Any Angle
7.5 Unit Circle Approach; Properties of the Trigonometric Functions
7.6 Graphs of the Sine and Cosine Functions
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
7.8 Phase Shift; Building Sinusoidal Models
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
8. Analytic Trigonometry
8.1 The Inverse Sine, Cosine, and Tangent Functions
8.2 The Inverse Trigonometric Functions (Continued)
8.3 Trigonometric Equations
8.4 Trigonometric Identities
8.5 Sum and Difference Formulas
8.6 Double-angle and Half-angle Formulas
8.7 Product-to-Sum and Sum-to-Product Formulas
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
9. Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles
9.2 The Law of Sines
9.3 The Law of Cosines
9.4 Area of a Triangle
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
10. Polar Coordinates; Vectors
10.1 Polar Coordinates
10.2 Polar Equations and Graphs
10.3 The Complex Plane; DeMoivre's Theorem
10.4 Vectors
10.5 The Dot Product
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
11. Analytic Geometry
11.1 Conics
11.2 The Parabola
11.3 The Ellipse
11.4 The Hyperbola
11.5 Rotation of Axes; General Form of a Conic
11.6 Polar Equations of Conics
11.7 Plane Curves and Parametric Equations
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
12. Systems of Equations and Inequalities
12.1 Systems of Linear Equations: Substitution and Elimination
12.2 Systems of Linear Equations: Matrices
12.3 Systems of Linear Equations: Determinants
12.4 Matrix Algebra
12.5 Partial Fraction Decomposition
12.6 Systems of Nonlinear Equations
12.7 Systems of Inequalities
12.8 Linear Programming
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
13. Sequences; Induction; the Binomial Theorem
13.1 Sequences
13.2 Arithmetic Sequences
13.3 Geometric Sequences; Geometric Series
13.4 Mathematical Induction
13.5 The Binomial Theorem
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
14. Counting and Probability
14.1 Counting
14.2 Permutations and Combinations
14.3 Probability
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
Answers
Index
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