College Algebra, Second Edition is a comprehensive presentation of the fundamental concepts and techniques of algebra. The book incorporates some improvements from the previous edition to provide a better learning experience. It provides sufficient materials for use in the study of college algebra. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, exponential and logarithmic functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter contains a summary, including terms and symbols with appropriate page references; key ideas for review to stress the concepts; review exercises to provide additional practice; and progress tests to provide self-evaluation and reinforcement. The answers to all Review Exercises and Progress Tests appear in the back of the book. College students will find the book very useful and invaluable.
Inhalt
Preface
Acknowledgments
To the Student
Chapter 1 The Foundations of Algebra
1.1 The Real Number System
1.2 The Real Number Line
1.3 Algebraic Expressions; Polynomials
1.4 Factoring
1.5 Rational Expressions
1.6 Integer Exponents
1.7 Rational Exponents and Radicals
Chapter 2 Equations And Inequalities
2.1 Linear Equations in One Unknown
2.2 Applications
2.3 Linear Inequalities
2.4 Absolute Value in Equations and Inequalities
2.5 The Quadratic Equation
2.6 Applications of Quadratic Equations
2.7 Second-Degree Inequalities
Chapter 3 Functions
3.1 The Rectangular Coordinate System
3.2 Functions and Function Notation
3.3 Graphs of Functions
3.4 Linear Functions
3.5 Direct and Inverse Variation (Optional)
3.6 Combining Functions; Inverse Functions
Chapter 4 Exponential and Logarithmic Functions
4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Fundamental Properties of Logarithms
4.4 Computing with Logarithms (Optional)
4.5 Exponential and Logarithmic Equations
Chapter 5 Analytic Geometry: The Conic Sections
5.1 Analytic Geometry
5.2 The Circle
5.3 The Parabola
5.4 The Ellipse and Hyperbola
5.5 Identifying the Conic Sections
Chapter 6 Systems of Equations and Inequalities
6.1 Systems of Equations
6.2 Solving by Elimination
6.3 Applications
6.4 Systems of Linear Equations in Three Unknowns
6.5 Systems of Linear Inequalities
6.6 Linear Programming (Optional)
Chapter 7 Matrices and Determinants
7.1 Matrices and Linear Systems
7.2 Matrix Operations and Applications (Optional)
7.3 Inverses of Matrices (Optional)
7.4 Determinants and Cramer's Rule
Chapter 8 Theory of Polynomials
8.1 Polynomial Division and Synthetic Division
8.2 The Remainder and Factor Theorems
8.3 Factors and Zeros
8.4 Real and Rational Zeros
8.5 Rational Functions and Their Graphs
Chapter 9 Topics in Algebra
9.1 Sequences and Sigma Notation
9.2 Arithmetic Sequences
9.3 Geometric Sequences
9.4 Mathematical Induction
9.5 The Binomial Theorem
9.6 Counting: Permutations and Combinations
9.7 Probability
Tables Appendix
Answers to Odd-Numbered Exercises, and to Review Exercises and Progress Tests
Solutions to Selected Review Exercises
Index