College Algebra

Note: Each chapter concludes with a Chapter Summary, Review Exercises, a Chapter Test, and Proofs in Mathematics. P. Prerequisites P.1 Real Numbers P.2 Exponents and Radicals P.3 Polynomials and Factoring P.4 Rational Expressions P.5 The Cartesian Plane P.6 Representing Data Graphically 1. Functions and Their Graphs Introduction to Library of Parent Functions 1.1 Graphs of Equations 1.2 Lines in the Plane 1.3 Functions 1.4 Graphs of Functions 1.5 Shifting, Reflection, and Stretching Graphs 1.6 Combinations of Functions 1.7 Inverse Functions 2. Solving Equations and Inequalities 2.1 Linear Equations and Problem Solving 2.2 Solving Equations Graphically 2.3 Complex Numbers 2.4 Solving Quadratic Equations Algebraically 2.5 Solving Other Types of Equations Algebraically 2.6 Solving Inequalities Algebraically and Graphically 2.7 Linear Models and Scatter Plots Cumulative Test: Chapters P-2 Progressive Summary: Chapters P-2 3. Polynomial and Rational Functions 3.1 Quadratic Functions 3.2 Polynomial Functions of Higher Degree 3.3 Real Zeros of Polynomial Functions 3.4 The Fundamental Theorem of Algebra 3.5 Rational Functions and Asymptotes 3.6 Graphs of Rational Functions 3.7 Quadratic Models 4. Exponential and Logarithmic Functions 4.1 Exponential Functions and Their Graphs 4.2 Logarithmic Functions and Their Graphs 4.3 Properties of Logarithms 4.4 Solving Exponential and Logarithmic Equations 4.5 Exponential and Logarithmic Models 4.6 Nonlinear Models Progressive Summary: Chapters P-4 5. Linear Systems and Matrices 5.1 Solving Systems of Equations 5.2 Systems of Linear Equations in Two Variables 5.3 Multivariable Linear Systems 5.4 Matrices and Systems of Equations 5.5 Operations with Matrices 5.6 The Inverse of a Square Matrix 5.7 The Determinant of a Square Matrix 5.8 Applications of Matrices and Determinants Cumulative Test: Chapters 3-5 6. Sequences, Series, and Probability 6.1 Sequences and Series 6.2 Arithmetic Sequences and Partial Sums 6.3 Geometric Sequences and Series 6.4 Mathematical Induction 6.5 The Binomial Theorem 6.6 Counting Principles 6.7 Probability 7. Conics and Parametric Equations 7.1 Circles and Parabolas 7.2 Ellipses 7.3 Hyperbolas 7.4 Parametric Equations Cumulative Test: Chapters 6-7 Progressive Summary: Chapters P-7 Appendix A. Technology Support Guide Appendix B. Concepts in Statistics B.1 Measures of Central Tendency and Dispersion B.2 Least Squares Regression Appendix C. Variation Appendix D. Solving Linear Equations and Inequalities Appendix E. Systems of Inequalities E.1 Solving Systems of Inequalities E.2 Linear Programming Appendix F. Study Capsules

Dr. Ron Larson is a professor of mathematics at the Pennsylvania State University, where he has taught since 1970. He is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored more than 30 software titles since 1990. Dr. Larson has also authored numerous acclaimed textbooks, including the best-selling calculus series coauthored with Dr. Bruce Edwards and published by Cengage. Dr. Larson received the 2017 William Holmes McGuffey Longevity Award for PRECALCULUS and for CALCULUS. He also received the 2018 Text and Academic Authors Association TEXTY Award for CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS. In addition, Dr. Larson received the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS -- a complete text on CD-ROM that was the first mainstream college textbook to be offered on the internet. The Pennsylvania State University, The Behrend College
Bio: Robert P. Hostetler received his Ph.D. in mathematics from The Pennsylvania State University in 1970. He has taught at Penn State for many years and has authored several calculus, precalculus, and intermediate algebra textbooks. His teaching specialties include remedial algebra, calculus, and math education, and his research interests include mathematics education and textbooks. Dr. Bruce H. Edwards is a professor of mathematics at the University of Florida. Dr. Edwards received his B.S. in mathematics from Stanford University and his Ph.D. in mathematics from Dartmouth College. He taught mathematics at a university near Bogot, Colombia, as a Peace Corps volunteer. While teaching at the University of Florida, Dr. Edwards has received many teaching awards, including Teacher of the Year in the College of Liberal Arts and Sciences, Liberal Arts and Sciences Student Council Teacher of the Year and the University of Florida Honors Program Teacher of the Year. He was selected by the Office of Alumni Affairs to be the Distinguished Alumni Professor for 1991-1993. Dr. Edwards has taught a variety of mathematics courses at the University of Florida, from first-year calculus to graduate-level classes in algebra and numerical analysis. He has been a frequent speaker at research conferences and meetings of the National Council of Teachers of Mathematics. He has also coauthored a wide range of award-winning mathematics textbooks with Dr. Ron Larson.

Note: Each chapter concludes with a Chapter Summary, Review Exercises, a Chapter Test, and Proofs in Mathematics.
P. Prerequisites
P.1 Real Numbers
P.2 Exponents and Radicals
P.3 Polynomials and Factoring
P.4 Rational Expressions
P.5 The Cartesian Plane
P.6 Representing Data Graphically
1. Functions and Their Graphs
Introduction to Library of Parent Functions
1.1 Graphs of Equations
1.2 Lines in the Plane
1.3 Functions
1.4 Graphs of Functions
1.5 Shifting, Reflection, and Stretching Graphs
1.6 Combinations of Functions
1.7 Inverse Functions
2. Solving Equations and Inequalities
2.1 Linear Equations and Problem Solving
2.2 Solving Equations Graphically
2.3 Complex Numbers
2.4 Solving Quadratic Equations Algebraically
2.5 Solving Other Types of Equations Algebraically
2.6 Solving Inequalities Algebraically and Graphically
2.7 Linear Models and Scatter Plots
Cumulative Test: Chapters P-2
Progressive Summary: Chapters P-2
3. Polynomial and Rational Functions
3.1 Quadratic Functions
3.2 Polynomial Functions of Higher Degree
3.3 Real Zeros of Polynomial Functions
3.4 The Fundamental Theorem of Algebra
3.5 Rational Functions and Asymptotes
3.6 Graphs of Rational Functions
3.7 Quadratic Models
4. Exponential and Logarithmic Functions
4.1 Exponential Functions and Their Graphs
4.2 Logarithmic Functions and Their Graphs
4.3 Properties of Logarithms
4.4 Solving Exponential and Logarithmic Equations
4.5 Exponential and Logarithmic Models
4.6 Nonlinear Models
Progressive Summary: Chapters P-4
5. Linear Systems and Matrices
5.1 Solving Systems of Equations
5.2 Systems of Linear Equations in Two Variables
5.3 Multivariable Linear Systems
5.4 Matrices and Systems of Equations
5.5 Operations with Matrices
5.6 The Inverse of a Square Matrix
5.7 The Determinant of a Square Matrix
5.8 Applications of Matrices and Determinants
Cumulative Test: Chapters 3-5
6. Sequences, Series, and Probability
6.1 Sequences and Series
6.2 Arithmetic Sequences and Partial Sums
6.3 Geometric Sequences and Series
6.4 Mathematical Induction
6.5 The Binomial Theorem
6.6 Counting Principles
6.7 Probability
7. Conics and Parametric Equations
7.1 Circles and Parabolas
7.2 Ellipses
7.3 Hyperbolas
7.4 Parametric Equations
Cumulative Test: Chapters 6-7
Progressive Summary: Chapters P-7
Appendix A. Technology Support Guide
Appendix B. Concepts in Statistics
B.1 Measures of Central Tendency and Dispersion
B.2 Least Squares Regression
Appendix C. Variation
Appendix D. Solving Linear Equations and Inequalities
Appendix E. Systems of Inequalities
E.1 Solving Systems of Inequalities
E.2 Linear Programming
Appendix F. Study Capsules