Algebra for College Students, Revised and Expanded Edition is a complete and self-contained presentation of the fundamentals of algebra which has been designed for use by the student. The book provides sufficient materials for use in many courses in college algebra. It contains chapters that are devoted to various mathematical concepts, such as the real number system, sets and set notation, matrices and their application in solving linear systems, and notation of functions. The theory of polynomial equations, formulas for factoring a sum and a difference of cubes, roots of polynomials, and the geometric definition of each conic are likewise included in the book. College students will find the book very useful and invaluable.
Inhalt
Preface
Acknowledgments
To the Student
Chapter One the REAL Number System
1.1 The Real Number System
1.2 Arithmetic Operations: Fractions
1.3 Algebraic Expressions
1.4 Operating with Signed Numbers
1.5 Properties of Real Numbers
1.6 Absolute Value and Inequalities
Chapter Two Polynomials
2.1 Polynomials
2.2 Addition and Subtraction of Polynomials
2.3 Multiplication of Polynomials
2.4 Factoring
2.5 Special Factors
Chapter Three Linear Equations and Inequalities
3.1 Linear Equations in One Variable
3.2 Applications
3.3 Linear Inequalities
3.4 Absolute Value in Equations and Inequalities
Chapter Four Word Problems
4.1 From Words to Algebra
4.2 Coin Problems
4.3 Investment Problems
4.4 Distance (Uniform Motion) Problems
4.5 Mixture Problems
Chapter Five Algebraic Fractions
5.1 Multiplication and Division of Fractions
5.2 Addition and Subtraction of Fractions
5.3 Complex Fractions
5.4 Ratio and Proportion
5.5 Equations and Inequalities with Fractions
5.6 Applications; Work Problems
Chapter Six Functions
6.1 Rectangular Coordinate Systems
6.2 Functions and Function Notation
6.3 Graphs of Functions
6.4 Increasing and Decreasing Functions
6.5 Direct and Inverse Variation
Chapter Seven the Straight Line
7.1 Slope of the Straight Line
7.2 Equations of the Straight Line
7.3 Further Properties of the Straight Line
7.4 Linear Inequalities in Two Variables
Chapter Eight Exponents, Radicals, and Complex Numbers
8.1 Positive Integer Exponents
8.2 Integer Exponents
8.3 Rational Exponents and Radicals
8.4 Evaluating and Simplifying Radicals
8.5 Operations with Radicals
8.6 Complex Numbers
Chapter Nine Second-Degree Equations and Inequalities
9.1 Solving Quadratic Equations
9.2 The Quadratic Formula
9.3 Roots of a Quadratic Equation: The Discriminant
9.4 Applications
9.5 Forms Leading to Quadratics
9.6 Second-Degree Inequalities
Chapter Ten Roots of Polynomials
10.1 Polynomial Division and Synthetic Division
10.2 The Remainder and Factor Theorems
10.3 Factors and Roots
10.4 Real and Rational Roots
Chapter Eleven Exponential and Logarithmic Functions
11.1 Combining Functions; Inverse Functions
11.2 Exponential Functions
11.3 Logarithmic Functions
11.4 Properties of Logarithms
11.5 Computing with Logarithms
11.6 Exponential and Logarithmic Equations
Chapter Twelve Analytic Geometry: The Conic Sections
12.1 Distance and Midpoint Formulas
12.2 Symmetry
12.3 The Circle
12.4 The Parabola
12.5 The Ellipse and Hyperbola
12.6 Identifying the Conic Sections
Chapter Thirteen Systems of Equations
13.1 Systems of Linear Equations
13.2 Solving by Elimination
13.3 Applications
13.4 Systems of Linear Equations in Three Unknowns
13.5 Systems Involving Nonlinear Equations
Chapter Fourteen Matrices and Determinants
14.1 Matrices and Linear Systems
14.2 Determinants
14.3 Cramer's Rule
Chapter Fifteen Topics in Algebra
15.1 Arithmetic Progressions
15.2 Geometric Progressions
15.3 The Binomial Theorem
15.4 Counting: Permutations and Combinations
Appendix/Tables
Answers to Odd-Numbered Exercises and Progress Tests
Index