Precalculus / Edition 2

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Overview

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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Product Details

  • ISBN-13: 9780077276508
  • Publisher: McGraw-Hill Higher Education
  • Publication date: 2/13/2009
  • Edition description: New Edition
  • Edition number: 2
  • Pages: 1216
  • Sales rank: 266,981
  • Product dimensions: 8.90 (w) x 11.00 (h) x 1.70 (d)

Meet the Author

John Coburn grew up in the Hawaiian Islands, the seventh of sixteen children. He received his Associate of Arts degree in 1977 from Windward Community College, where he graduated with honors. In 1979 he received a Bachelor’s Degree in Education from the University of Hawaii. After being lured into the business world for five years, he returned to his first love, accepting a teaching position in high school mathematics where he was recognized as Teacher of the Year in 1987. Soon afterward, the decision was made to seek a Masters Degree, which he received two years later from the University of Oklahoma. For the last fifteen years, he has been teaching mathematics at the Florissant Valley campus of St. Louis Community College, where he is now a full professor. During his tenure there he has received numerous nominations as an outstanding teacher by the local chapter of Phi Theta Kappa, two nominations to Who’s Who Among America’s Teachers and was recognized as Teacher of the year in 2004 by the Mathematics Educators of Greater St. Louis (MEGSL). He has made numerous presentations and local, state and national conferences on a wide variety of topics. His other loves include his family, music, athletics, games and all things beautiful, and hopes this love of life comes through in his writing, and serves to make the learning experience an interesting and engaging one for all students.

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Table of Contents

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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