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This text is for a one-term course in intermediate algebra, for students who have had a previous elementary algebra course. A five- step problem-solving process is introduced, and interesting applications are used to motivate students. Coverage progresses from graphs, functions, and linear equations to sequences, series, and the binomial theorem. New to this edition are sections on connecting concepts, study tips, and exercises designed to foster intuitive problem solving. Bittinger teaches at Indiana University; Ellenbogen at Community College of Vermont.
Table of Contents
1. Algebraic and Problem Solving
Some Basics of Algebra
Operations and Properties of Real Numbers
Solving Equations
Introduction to Problem Solving
Formulas, Models, and Geometry
Properties of Exponents
Scientific Notation
2. Graphs, Functions, and Linear Equations
Graphs
Functions
Linear Functions: Slope, Graphs, and Models
Another Look at Linear Graphs
Other Equations of Lines
The Algebra of Functions
3. Introduction to Graphing
Systems of Equations in Two Variables
Solving by Substitution or Elimination
Solving Applications: Systems of Two Equations
Systems of Equations in Three Variables
Solving Applications: Systems of Three Variables
Elimination Using Matrices
Determinants and Cramer's Rule
Business and Economics Applications
4. Inequalities and Problem Solving
Inequalities and Applications
Intersections, Unions, and Compound Inequalities
Absolute-Value Equations and Inequalities
Inequalities in Two Variables
Applications Using Linear Programming
5. Polynomials and Polynomial Functions
Introduction to Polynomials and Polynomial Functions
Multiplication of Polynomials
Common Factors and Factoring by Grouping
Factoring Trinomials
Factoring Perfect-Square Trinomials and Differences of Squares
Factoring Sums or Differences of Cubes
Factoring: A General Strategy
Applications of Polynomial Equations
6. Rational Expressions, Equations, and Functions
Rational Expressions and Functions: Multiplying and Dividing
Rational Expressions and Functions: Adding and Subtracting
Complex Rational Expressions
Rational Equations
Solving Applications Using Rational Equations
Division of Polynomials
Synthetic Division
Formulas, Applications, and Variation
7. Exponents and Radicals
Radical Expressions and Functions
Rational Numbers as Exponents
Multiplying Radical Expressions
Dividing Radical Expressions
Expressions Containing Several Radical Terms
Solving Radical Equations
The Distance and Midpoint Formulas and Other Applications
The Complex Numbers
8. Quadratic Functions and Equations
Quadratic Equations
The Quadratic Formula
Studying Solutions of Quadratic Equations
Applications Involving Quadratic Equations
Equations Reducible to Quadratic
Quadratic Functions and Their Graphs
More About Graphing Quadratic Functions
Problem Solving and Quadratic Functions
Polynomial and Rational Inequalities
9. Exponential and Logarithmic Functions
Composite and Inverse Functions
Exponential Functions
Logarithmic Functions
Properties of Logarithmic Functions
Common and Natural Logarithms
Solving Exponential and Logarithmic Equations
Applications of Exponential and Logarithmic Functions
10. Conic Sections
Conic Sections: Parabolas and Circles
Conic Sections: Ellipses
Conic Sections: Hyperbolas
Nonlinear Systems of Equations
11. Sequences, Series, and the Binomial Theorem
Sequences and Series
Arithmetic Sequences and Series
Geometric Sequences and Series
The Binomial Theorem
Appendix: The Graphing Calculator
Answers A-1
Glossary EM-1
Index EM-6
Index of Applications EM-13
This text is for a one-term course in intermediate algebra, for students who have had a previous elementary algebra course. A five- step problem-solving process is introduced, and interesting applications are used to motivate students. Coverage progresses from graphs, functions, and linear equations to sequences, series, and the binomial theorem. New to this edition are sections on connecting concepts, study tips, and exercises designed to foster intuitive problem solving. Bittinger teaches at Indiana University; Ellenbogen at Community College of Vermont.
Table of Contents
Table of Contents
1. Algebraic and Problem Solving
Some Basics of Algebra
Operations and Properties of Real Numbers
Solving Equations
Introduction to Problem Solving
Formulas, Models, and Geometry
Properties of Exponents
Scientific Notation
2. Graphs, Functions, and Linear Equations
Graphs
Functions
Linear Functions: Slope, Graphs, and Models
Another Look at Linear Graphs
Other Equations of Lines
The Algebra of Functions
3. Introduction to Graphing
Systems of Equations in Two Variables
Solving by Substitution or Elimination
Solving Applications: Systems of Two Equations
Systems of Equations in Three Variables
Solving Applications: Systems of Three Variables
Elimination Using Matrices
Determinants and Cramer's Rule
Business and Economics Applications
4. Inequalities and Problem Solving
Inequalities and Applications
Intersections, Unions, and Compound Inequalities
Absolute-Value Equations and Inequalities
Inequalities in Two Variables
Applications Using Linear Programming
5. Polynomials and Polynomial Functions
Introduction to Polynomials and Polynomial Functions
Multiplication of Polynomials
Common Factors and Factoring by Grouping
Factoring Trinomials
Factoring Perfect-Square Trinomials and Differences of Squares
Factoring Sums or Differences of Cubes
Factoring: A General Strategy
Applications of Polynomial Equations
6. Rational Expressions, Equations, and Functions
Rational Expressions and Functions: Multiplying and Dividing
Rational Expressions and Functions: Adding and Subtracting
Complex Rational Expressions
Rational Equations
Solving Applications Using Rational Equations
Division of Polynomials
Synthetic Division
Formulas, Applications, and Variation
7. Exponents and Radicals
Radical Expressions and Functions
Rational Numbers as Exponents
Multiplying Radical Expressions
Dividing Radical Expressions
Expressions Containing Several Radical Terms
Solving Radical Equations
The Distance and Midpoint Formulas and Other Applications
The Complex Numbers
8. Quadratic Functions and Equations
Quadratic Equations
The Quadratic Formula
Studying Solutions of Quadratic Equations
Applications Involving Quadratic Equations
Equations Reducible to Quadratic
Quadratic Functions and Their Graphs
More About Graphing Quadratic Functions
Problem Solving and Quadratic Functions
Polynomial and Rational Inequalities
9. Exponential and Logarithmic Functions
Composite and Inverse Functions
Exponential Functions
Logarithmic Functions
Properties of Logarithmic Functions
Common and Natural Logarithms
Solving Exponential and Logarithmic Equations
Applications of Exponential and Logarithmic Functions
10. Conic Sections
Conic Sections: Parabolas and Circles
Conic Sections: Ellipses
Conic Sections: Hyperbolas
Nonlinear Systems of Equations
11. Sequences, Series, and the Binomial Theorem
Sequences and Series
Arithmetic Sequences and Series
Geometric Sequences and Series
The Binomial Theorem
Appendix: The Graphing Calculator
Answers A-1
Glossary EM-1
Index EM-6
Index of Applications EM-13