9780078092404

Three components contribute to a theme sustained throughout the Coburn Series: that of laying a firm foundation, building a solid framework, and providing strong connections. Not only does Coburn present a sound problem-solving process to teach students to recognize a problem, organize a procedure, and formulate a solution, the text encourages students to see beyond procedures in an effort to gain a greater understanding of the big ideas behind mathematical concepts. Written in a readable, yet mathematically mature manner appropriate for college algebra level students, Coburn's Precalculus uses narrative, extensive examples, and a range of exercises to connect seemingly disparate mathematical topics into a cohesive whole. Coburn's hallmark applications are born out of the author's extensive experiences in and outside the classroom, and appeal to the vast diversity of students and teaching methods in this course area. Benefiting from the feedback of hundreds of instructors and students across the country, Precalculus second edition, continues to emphasize connections in order to improve the level of student engagement in mathematics and increase their chances of success in college algebra.

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Chapter 1: Equations and Inequalities

1-1 Linear Equations, Formulas, and Problem Solving
1-2 Linear Inequalities in One Variable
1-3 Absolute Value Equations and Inequalities
1-4 Complex Numbers
1-5 Solving Quadratic Equations
1-6 Solving Other Types of Equations
Chapter 2: Relations, Functions and Graphs
2-1 Rectangular Coordinates; Graphing Circles and Relations
2-2 Graphs of Linear Equations
2-3 Linear Equations and Rates of Change
2-4 Functions, Notation, and Graphs of Functions
2-5 Analyzing the Graph of a Function
2-6 Toolbox Functions and Transformations
2-7 Piecewise-Defined Functions
2-8 The Algebra and Composition of Functions
Chapter 3: Polynomial and Rational Functions
3-1 Quadratic Functions and Applications
3-2 Synthetic Division; The Remainder and Factor Theorems
3-3 The Zeroes of Polynomial Functions
3-4 Graphing Polynomial Functions
3-5 Graphing Rational Functions
3-6 Additional Insights into Rational Functions
3-7 Polynomial and Rational Inequalities
3-8 Variation: Function Models in Action
Chapter 4: Exponential and Logarithmic Functions
4-1 One-to-One and Inverse Functions
4-2 Exponential Functions
4-3 Logarithms and Logarithmic Functions
4-4 Properties of Logarithms; Solving Exponential and Logarithmic Equations
4-5 Applications from Business, Finance, and Science
Chapter 5: Introduction to Trigonometric Functions
5-1 Angle Measure, Special Triangles, and Special Angles
5-2 Unit Circles and the Trigonometry of Real Numbers
5-3 Graphs of Sine and Cosine Functions; Cosecant and Secant Functions
5-4 Graphs of Tangent and Cotangent Functions
5-5 Transformations and Applications of Trigonometric Graphs
5-6 The Trigonometry of Right Triangles
5-7 Trigonometry and the Coordinate Plane
Chapter 6: Trigonometric Identities, Inverses, and Equations
6-1 Fundamental Identities and Families of Identities
6-2 Constructing and Verifying Identities
6-3 The Sum and Difference Identities
6-4 Double Angle, Half Angle & Product-to-Sum Identities
6-5 The Inverse Trigonometric Functions and Their Applications
6-6 Solving Basic Trigonometric Equations
6-7 General Trigonometric Equations and Applications
Chapter 7: Applications of Trigonometry
7-1 Oblique Triangles and the Law of Sines
7-2 The Law of Cosines; Area of a Triangle
7-3 Vectors and Vector Diagrams
7-4 Vector Applications and the Dot Product
7-5 Complex Numbers in Trigonometric Form
7-6 Demoivre’s Theorem and the Theorem on nth Roots
Chapter 8: Systems of Equations and Inequalities
8-1 Linear Systems in Two Variables with Applications
8-2 Linear Systems in Three Variables with Applications
8-3 Partial Fraction Decomposition
8-4 Systems of Inequalities and Linear Programming
8-5 Solving Systems Using Matrices and Row Operations
8-6 The Algebra of Matrices
8-7 Solving Linear Systems Using Matrix Equations
8-8 Applications of Matrices and Determinants: Cramer's Rule, Geometry, and More
Chapter 9: Analytical Geometry
9-1 Introduction to Analytic Geometry
9-2 The Circle and the Ellipse
9-3 The Hyperbola
9-4 The Analytic Parabola
9-5 Nonlinear Systems of Equations and Inequalities
9-6 Polar Coordinates, Equations, and Graphs
9-7 More on Conic Sections: Rotation of Axes and Polar Form
9-8 Parametric Equations and Graphs
Chapter 10: Additional Topics in Algebra
10-1 Sequences and Series
10-2 Arithmetic Sequences
10-3 Geometric Sequences
10-4 Mathematical Induction
10-5 Counting Techniques
10-6 Introduction to Probability
10-7 The Binomial Theorem
Chapter 11: Bridges to Calculus - An Introduction to Limits
11-1 Finding Limits Numerically and Graphically
11-2 Algebraic Methods for Finding Limits; One-Sided Limits and Continuity
11-3 Infinite Limits and Limits at Infinity
11-4 Applications of Limits: Instantaneous Rates of Change and the Area Under a Curve
APPENDICES
A-1 A Review of Basic Concepts and Skills
A-2 US Standard Units and the Metric System
A-3 Rational Expressions and the Least Common Denominator
A-4 Deriving the Equation of a Conic
A-5 More on Matrices
A-6 Deriving the Equation of a Conic

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Combo: Precalculus with ALEKS User Guid & Access Code 1 Semester

Combo: Precalculus with ALEKS User Guid & Access Code 1 Semester

007809240X

Summary

Table of Contents

Chapter 1: Equations and Inequalities

1-2 Linear Inequalities in One Variable

1-3 Absolute Value Equations and Inequalities

1-4 Complex Numbers

1-5 Solving Quadratic Equations

1-6 Solving Other Types of Equations

Chapter 2: Relations, Functions and Graphs

2-1 Rectangular Coordinates; Graphing Circles and Relations

2-2 Graphs of Linear Equations

2-3 Linear Equations and Rates of Change

2-4 Functions, Notation, and Graphs of Functions

2-5 Analyzing the Graph of a Function

2-6 Toolbox Functions and Transformations

2-7 Piecewise-Defined Functions

2-8 The Algebra and Composition of Functions

Chapter 3: Polynomial and Rational Functions

3-1 Quadratic Functions and Applications

3-2 Synthetic Division; The Remainder and Factor Theorems

3-3 The Zeroes of Polynomial Functions

3-4 Graphing Polynomial Functions

3-5 Graphing Rational Functions

3-6 Additional Insights into Rational Functions

3-7 Polynomial and Rational Inequalities

3-8 Variation: Function Models in Action

Chapter 4: Exponential and Logarithmic Functions

4-1 One-to-One and Inverse Functions

4-2 Exponential Functions

4-3 Logarithms and Logarithmic Functions

4-4 Properties of Logarithms; Solving Exponential and Logarithmic Equations

4-5 Applications from Business, Finance, and Science

Chapter 5: Introduction to Trigonometric Functions

5-1 Angle Measure, Special Triangles, and Special Angles

5-2 Unit Circles and the Trigonometry of Real Numbers

5-3 Graphs of Sine and Cosine Functions; Cosecant and Secant Functions

5-4 Graphs of Tangent and Cotangent Functions

5-5 Transformations and Applications of Trigonometric Graphs

5-6 The Trigonometry of Right Triangles

5-7 Trigonometry and the Coordinate Plane

Chapter 6: Trigonometric Identities, Inverses, and Equations

6-1 Fundamental Identities and Families of Identities

6-2 Constructing and Verifying Identities

6-3 The Sum and Difference Identities

6-4 Double Angle, Half Angle & Product-to-Sum Identities

6-5 The Inverse Trigonometric Functions and Their Applications

6-6 Solving Basic Trigonometric Equations

6-7 General Trigonometric Equations and Applications

Chapter 7: Applications of Trigonometry

7-1 Oblique Triangles and the Law of Sines

7-2 The Law of Cosines; Area of a Triangle

7-3 Vectors and Vector Diagrams

7-4 Vector Applications and the Dot Product

7-5 Complex Numbers in Trigonometric Form

7-6 Demoivre’s Theorem and the Theorem on nth Roots

Chapter 8: Systems of Equations and Inequalities

8-1 Linear Systems in Two Variables with Applications

8-2 Linear Systems in Three Variables with Applications

8-3 Partial Fraction Decomposition

8-4 Systems of Inequalities and Linear Programming

8-5 Solving Systems Using Matrices and Row Operations

8-6 The Algebra of Matrices

8-7 Solving Linear Systems Using Matrix Equations

8-8 Applications of Matrices and Determinants: Cramer's Rule, Geometry, and More

Chapter 9: Analytical Geometry

9-1 Introduction to Analytic Geometry

9-2 The Circle and the Ellipse

9-3 The Hyperbola

9-4 The Analytic Parabola

9-5 Nonlinear Systems of Equations and Inequalities

9-6 Polar Coordinates, Equations, and Graphs

9-7 More on Conic Sections: Rotation of Axes and Polar Form

9-8 Parametric Equations and Graphs

Chapter 10: Additional Topics in Algebra

10-1 Sequences and Series