Loose Leaf Version for Precalculus: Graphs & Models

by John W. Coburn, J.D. (John) Herdlick

Overview

Three components contribute to a theme sustained throughout the Coburn/Herdlick Graphs and Models series: that of laying a firm foundation, building a solid framework, and providing strong connections. In the Graphs and Models texts, the authors combine their depth of experience with the conversational style and the wealth of applications that the Coburn/Herdlick texts have become known for. By combining a graphical approach to problem solving with algebraic methods, students learn how to relate their mathematical knowledge to the outside world. The authors use technology to solve the more true to life equations, to engage more applications, and to explore the more substantial questions involving graphical behavior. Benefiting from the feedback of hundreds of instructors and students across the country, Precalculus: Graphs & Models emphasizes connections in order to improve the level of student engagement in mathematics and increase their chances of success in precalculus and calculus.

The launch of the Coburn/Herdlick Graphs and Models series provides a significant leap forward in terms of online course management with McGraw-Hill’s new homework platform, Connect Math Hosted by ALEKS Corp. Math instructors served as digital contributors to choose the problems that will be available, authoring each algorithm and providing stepped out solutions that go into great detail and are focused on areas where students commonly make mistakes. From there, the ALEKS Corporation reviewed each algorithm to ensure accuracy. A unifying theme throughout the entire process was the involvement of the authors. Through each step, they provided feedback and guidance to the digital contributors to ensure that the content being developed digitally closely matched the textbook. The result is an online homework platform that provides superior content and feedback, allowing students to effectively learn the material being taught.

Product Details

ISBN-13:	9780077431181
Publisher:	McGraw Hill LLC
Publication date:	03/10/2011
Pages:	2912
Product dimensions:	8.40(w) x 10.90(h) x 1.80(d)

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.

Table of Contents

Precalculus: Graphs & Models
Chapter 1: Functions and Graphs
Rectangular Coordinates, Graphing Circles and Other Relations
Functions, Function Notation, and the Graph of a Function
Linear Equations and Rates of Change
Linear Functions, Special Forms, and More on Rates of Change
Solving Equations and Inequalities Graphically; Formulas and Problem Solving
Linear Models and Real Data
Chapter 2: Relations, More on Functions
Analyzing the Graph of a Function
The Toolbox Functions and Transformations
Absolute Value Functions, Equations, and Inequalities
Rational and Radical Functions; More on the Domain
Piecewise-Defined Functions
Variation: The Toolbox Functions in Action
Chapter 3: Quadratic Functions and Operations on Functions
complex Numbers
Solving Quadratic Equations and Inequalities
Quadratic Functions and Applications
Quadratic Models; More on Rates of Change
The Algebra of Functions
Composition of Functions and the Difference Quotient
Chapter 4: Polynomial and Rational Functions
Synthetic Division; the Remainder and Factor Theorems
The Zeros of Polynomial Functions
Graphing Polynomial Functions
Graphing Rational Functions
Additional Insights into Rational Functions
Polynomial and Rational Inequalities
Chapter 5: Exponential and Logarithmic Functions
One-to-One and Inverse Functions
Exponential Functions
Logarithms and Logarithmic Functions
Properties of Logarithms
Solving Exponential/Logarithmic Equations
Applications from Business, Finance, and Science
Exponential, Logarithmic, and Logistic Equation Models
Chapter 6: Introduction to Trigonometry
Angle Measure, Special Triangles, and Special Angles
Unit Circles and the Trigonometry of Real Numbers
Graphs of Sine and Cosine Functions
Graphs of the Cosecant, Secant, Tangent, and Cotangent Functions
Translations and Applications of Trigonometric Graphs
The Trigonometry of Right Triangles
Trigonometry and the Coordinate Plane
Chapter 7: Trigonometric Identities, Inverses, and Equations
Fundamental Identities and Families of Identities
Constructing and Verifying Identities
The Sum and Difference Identities
Double Angle, Half Angle and Product-to-Sum Identities
Inverse Trigonometric Functions and their Applications
Solving Basic Trig Equations
General Trig Equations and Applications
Chapter 8: Applications of Trigonometry
Oblique Triangles and the Law of Sines
The Law of Cosines; the Area of a Triangle
Vectors and Vector Diagrams
Vectors Applications and the Dot Product
Complex Numbers in Trigonometric Form
DeMoivre’s Theorem and the Theorem on Nth Roots
Chapter 9: Systems of Equations ad Inequalities; Matrices
Systems of Equations in Two Variables
Systems of Equations in Three Variables
Partial Fraction Decomposition
Linear Inequalities and Linear Programming
Matrices and Row Operations
The Algebra of Matrices
Linear Systems and Matrix Equations
Applications of Matrices and Determinants
Chapter 10: Analytical Geometry; Polar and Parametric Equations
An Introduction to Analytic Geometry
The Circle and the Ellipse
The Hyperbola
The Analytic Parabola
Non-Linear Systems of Equations and Inequalities
Polar Coordinates, Equations, and Graphs
Rotation of Axes and Polar Form
Parametric Equations and Graphs
Chapter 11: Sequences, Series, Counting, and Probability
Sequences and Series
Arithmetic Sequences
Geometric Sequences
Mathematical Induction
Counting Techniques
Introduction to Probability
The Binomial Theorem
Chapter 12: Bridges to Calculus – An Introduction to Limits
Finding Limits Numerically and Graphically
Algebraic Methods for Finding Limits; One-Sided Limits and Continuity
Infinite Limits and Limits at Infinity
Applications of Limits: Instantaneous Rates of Change and the Area Under a Curve
Appendix A: A Review of Basic Concepts and Skills
The Language, Notation, and Numbers of Mathematics
Algebraic Expressions, and the Properties of Real Numbers
Exponents, Scientific Notation, and a Review of Polynomials
Solving Linear Equations
Factoring Polynomials and Solving Equations by Factoring
Rational Expressions and Equations
Radicals, Rational Exponents, and Radical Equations
Geometry Review with Unit Conversions
Appendix B: Proof Positive!
Appendix C: More on Synthetic Division
Appendix D: Reduced Row-Echelon Form and More on Matrices
Appendix E: The Equation of a Conic
Appendix F: Sinusoidal Regression Models