Precalculus

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.

List of contents

Chapter 1: Equations and Inequalities

1-1Linear Equations, Formulas, and Problem Solving

1-2Linear Inequalities in One Variable

1-3Absolute Value Equations and Inequalities

1-4Complex Numbers

1-5Solving Quadratic Equations

1-6Solving Other Types of EquationsChapter 2: Relations, Functions and Graphs

2-1Rectangular Coordinates; Graphing Circles and Relations

2-2Graphs of Linear Equations

2-3Linear Equations and Rates of Change

2-4Functions, Notation, and Graphs of Functions

2-5Analyzing the Graph of a Function

2-6Toolbox Functions and Transformations

2-7Piecewise-Defined Functions

2-8The Algebra and Composition of FunctionsChapter 3: Polynomial and Rational Functions

3-1Quadratic Functions and Applications

3-2Synthetic Division; The Remainder and Factor Theorems

3-3The Zeroes of Polynomial Functions

3-4Graphing Polynomial Functions

3-5Graphing Rational Functions

3-6Additional Insights into Rational Functions

3-7Polynomial and Rational Inequalities

3-8Variation: Function Models in ActionChapter 4: Exponential and Logarithmic Functions

4-1One-to-One and Inverse Functions

4-2Exponential Functions

4-3Logarithms and Logarithmic Functions

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

4-5Applications from Business, Finance, and ScienceChapter 5: Introduction to Trigonometric Functions

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

5-2Unit Circles and the Trigonometry of Real Numbers

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

5-4Graphs of Tangent and Cotangent Functions

5-5Transformations and Applications of Trigonometric Graphs5-6The Trigonometry of Right Triangles

5-7Trigonometry and the Coordinate Plane Chapter 6: Trigonometric Identities, Inverses, and Equations

6-1Fundamental Identities and Families of Identities

6-2Constructing and Verifying Identities

6-3The Sum and Difference Identities

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

6-5The Inverse Trigonometric Functions and Their Applications

6-6Solving Basic Trigonometric Equations

6-7General Trigonometric Equations and ApplicationsChapter 7: Applications of Trigonometry

7-1Oblique Triangles and the Law of Sines

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

7-3Vectors and Vector Diagrams

7-4Vector Applications and the Dot Product

7-5Complex Numbers in Trigonometric Form

7-6Demoivre's Theorem and the Theorem on nth Roots Chapter 8: Systems of Equations and Inequalities

8-1Linear Systems in Two Variables with Applications

8-2Linear Systems in Three Variables with Applications

8-3Partial Fraction Decomposition

8-4Systems of Inequalities and Linear Programming

8-5Solving Systems Using Matrices and Row Operations

8-6The Algebra of Matrices

8-7Solving Linear Systems Using Matrix Equations

8-8Applications of Matrices and Determinants: Cramer's Rule, Geometry, and MoreChapter 9: Analytical Geometry

9-1Introduction to Analytic Geometry

9-2The Circle and the Ellipse

9-3The Hyperbola

9-4The Analytic Parabola

9-5Nonlinear Systems of Equations and Inequalities

9-6Polar Coordinates, Equations, and Graphs

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

9-8Parametric Equations and GraphsChapter 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-1A Review of Basic Concepts and Skills

A-2US Standard Units and the Metric System

A-3Rational Expressions and the Least Common Denominator

A-4Deriving the Equation of a Conic

A-5More on Matrices

A-6Deriving the Equation of a Conic

About 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.

Summary

Improve the level of student engagement! Text emphasizes connections and problem solving.

Product details

• Authors: John Coburn, John W Coburn, John W. Coburn, Coburn John
• Publisher: McGraw-Hill
• Languages: English
• Product format: Hardback
• Released: 16.03.2009
• EAN: 9780077276508
• ISBN: 978-0-07-727650-8
• No. of pages: 1072
• Dimensions: 224 mm x 282 mm x 46 mm
• Weight: 2520 g
• Illustrations: farbige Illustrationen, Zahlen
• Series: Collegiate Math
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; MATHEMATICS / Mathematical Analysis, Calculus & mathematical analysis, Calculus and mathematical analysis