College Algebra & Trigonometry / Edition 1

by Julie Miller, Donna Gerken

Overview

Julie Miller wrote her developmental math series because students were coming into her Precalculus course underprepared. They weren’t mathematically mature enough to understand the concepts of math nor were they fully engaged with the material. She began her developmental mathematics offerings with intermediate algebra to help bridge that gap. The Precalculus series is a carefully constructed end to that bridge that uses the highly effective pedagogical features from her fastest growing developmental math series. What sets Julie Miller’s series apart is that it addresses course issues through an author-created digital package that maintains a consistent voice and notation throughout the program. This consistency—in videos, PowerPoints, Lecture Notes, and Group Activities—coupled with the power of ALEKS and Connect Hosted by ALEKS, ensures that students master the skills necessary to be successful in Precalculus and can carry them through to the calculus sequence.

Product Details

ISBN-13:	9780078035623
Publisher:	McGraw Hill LLC
Publication date:	01/04/2016
Edition description:	New Edition
Pages:	1264
Product dimensions:	8.90(w) x 11.10(h) x 1.70(d)
Age Range:	18 Years

About the Author

Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers.
My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I can remember using graph paper to plot data points for his experiments and doing simple calculations. He would then tell me what the peaks and features in the graph meant in the context of his experiment. I think that applications and hands-on experience made math come alive for me and I’d like to see math come alive for my students.

Table of Contents

SectionR.1Sets and the Real Number Line SectionR.2Integer Exponents and Scientific Notation SectionR.3Rational Exponents and Radicals SectionR.4Polynomials and Multiplication of Radicals Problem Recognition Exercises Simplifying Algebraic Expressions SectionR.5Factoring SectionR.6Rational Expressions and More Operations on Radicals Algebra for Calculus Section1.1Linear Equations and Rational Equations Section1.2Applications with Linear and Rational Equations Section1.3Complex Numbers Section1.4Quadratic Equations Problem Recognition Exercises Simplifying Expressions Versus Solving Equations Section 1.5Applications of Quadratic Equations Section1.6More Equations and Applications Section1.7Linear, Compound, and Absolute Value Inequalities Problem Recognition Exercises Recognizing and Solving Equations and Inequalities Equations for Calculus Section2.1The Rectangular Coordinate System and Graphing Utilities Section2.2Circles Section2.3Functions and Relations Section2.4Linear Equations in Two Variables and Linear Functions Section2.5Applications of Linear Equations and Modeling Problem Recognition Exercises Comparing Graphs of Equations Section2.6Transformations of Graphs Section2.7Analyzing Graphs of Functions and Piecewise-Defined Functions Section2.8Algebra of Functions and Function Composition Section3.1Quadratic Functions and Applications Section3.2Introduction to Polynomial Functions Section3.3Division of Polynomials and the Remainder and Factor Theorems Section3.4Zeros of Polynomials Section3.5Rational Functions Problem Recognition Exercises Polynomial and Rational Functions Section3.6Polynomial and Rational Inequalities Problem Recognition Exercises Solving Equations and Inequalities Section3.7Variation Section4.1Inverse Functions Section4.2Exponential Functions Section4.3Logarithmic Functions Problem Recognition Exercises Analyzing Functions Section4.4Properties of Logarithms Section4.5Exponential and Logarithmic Equations Section4.6Modeling with Exponential and Logarithmic Functions Section5.1Angles and Their Measure Section5.2Right Triangle Trigonometry Section5.3Trigonometric Functions of Any Angle Section5.4Trigonometric Functions Defined on the Unit Circle Section5.5Graphs of Sine and Cosine Functions Section5.6Graphs of Other Trigonometric Functions Problem Recognition Exercises Comparing Graphical Characteristics of Trigonometric Functions Section5.7Inverse Trigonometric Functions Section6.1Fundamental Trigonometric Identities Section6.2Sum and Difference Formulas Section6.3Double-Angle and Half-Angle Formulas Section6.4Product-to-Sum and Sum-to-Product Formulas Section6.5Trigonometric Equations Section7.1Applications of Right Triangles Section7.2The Law of Sines Section7.3The Law of Cosines Problem Recognition Exercises Solving Triangles Using a Variety of Tools Section7.4Harmonic Motion and Combinations of Trigonometric Functions Section8.1Polar Coordinates Section8.2Graphs of Polar Equations Problem Recognition Exercises Comparing Equations in Polar and Rectangular Form Section 8.3Complex Numbers in Polar Form Section8.4Vectors Section8.5Dot Product Section9.1Systems of Linear Equations in Two Variables and Applications Section9.2Systems of Linear Equations in Three Variables and Applications Section9.3Partial Fraction Decomposition Section9.4Systems of Nonlinear Equations in Two Variables Section9.5Inequalities and Systems of Inequalities in Two Variables Problem Recognition Exercises Equations and Inequalities in Two Variables Section9.6Linear Programming Section10.1Solving Systems of Linear Equations Using Matrices Section10.2Inconsistent Systems and Dependent Equations Section10.3Operations on Matrices Section10.4Inverse Matrices and Matrix Equations Section10.5Determinants and Cramer's Rule Problem Recognition Exercises Using Multiple Methods to Solve Systems of Linear Equations Section11.1The Ellipse Section11.2The Hyperbola Section11.3The Parabola Problem Recognition Exercises Comparing Equations of Conic Sections and General Equation Section11.4Rotation of Axes Section11.5Polar Equations of Conics Section11.6Plane Curves and Parametric Equations Section12.1Sequences and Series Section12.2Arithmetic Sequences and Series Section12.3Geometric Sequences and Series Problem Recognition Exercises Comparing Arithmetic and Geometric Sequences and Series Section12.4Mathematical Induction Section12.5The Binomial Theorem Section12.6Principles of Counting Section12.7Introduction to Probability