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Algebra For College Students,9780538733540

Algebra For College Students

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Pub. Date:
Cengage Learning
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Kaufmann and Schwitters have built this text's reputation on clear and concise exposition, numerous examples, and plentiful problem sets. This traditional text consistently reinforces the following common thread: learn a skill; practice the skill to help solve equations; and then apply what you have learned to solve application problems. This simple, straightforward approach has helped many students grasp and apply fundamental problem solving skills necessary for future mathematics courses. Algebraic ideas are developed in a logical sequence, and in an easy-to-read manner, without excessive vocabulary and formalism. The open and uncluttered design helps keep students focused on the concepts while minimizing distractions. Problems and examples reference a broad range of topics, as well as career areas such as electronics, mechanics, and health, showing students that mathematics is part of everyday life.

Table of Contents

Basic Concepts and Properties
Sets, Real Numbers, and Numerical Expressions
Operations with Real Numbers
Properties of Real Numbers and the Use of Exponents
Algebraic Expressions
Chapter 1 Summary
Chapter 1 Review Problem Set
Chapter 1 Test
Equations, Inequalities, and Problem Solving
Solving First-Degree Equations
Equations Involving Fractional Forms
Equations Involving Decimals and Problem Solving
More on Inequalities and Problem Solving
Equations and Inequalities Involving Absolute Value
Chapter 2 Summary
Chapter 2 Review Problem Set
Chapter 2 Test
Polynomials: Sums and Differences
Products and Quotients of Monomials
Multiplying Polynomials
Factoring: Use of the Distributive Property
Factoring: Difference of Two Squares and Sum or Difference of Two Cubes
Factoring Trinomials
Equations and Problem Solving
Chapter 3 Summary
Chapter 3 Review Problem Set
Chapter 3 Test
Cumulative Review Problem Set (Chapters 1-3)
Rational Expressions
Simplifying Rational Expressions
Multiplying and Dividing Rational Expressions
Adding and Subtracting Rational Expressions
More on Rational Expressions and Complex Fractions
Dividing Polynomials
Fractional Equations
More Fractional Equations and Applications
Chapter 4 Summary
Chapter 4 Review Problem Set
Chapter 4 Test
Exponents and Radicals
Using Integers as Exponents
Roots and Radicals
Combining Radicals and Simplifying Radicals That Contain Variables
Products and Quotients Involving Radicals
Equations Involving Radicals
Merging Exponents and Roots
Scientific Notation
Chapter 5 Summary
Chapter 5 Review Problem Set
Chapter 5 Test
Quadratic Equations and Inequalities
Complex Numbers
Quadratic Equations
Completing the Square
Quadratic Formula
More Quadratic Equations and Applications
Quadratic and Other Nonlinear Inequalities
Chapter 6 Summary
Chapter 6 Review Problem Set
Chapter 6 Test
Cumulative Review Problem Set (Chapters 1- 6)
Linear Equations and Inequalities in Two Variables
Rectangular Coordinate System and Linear Equations
Graphing Nonlinear Equations
Linear Inequalities in Two Variables
Distance and Slope
Determining the Equation of a Line
Chapter 7 Summary
Chapter 7 Review Problem Set
Chapter 7 Test
Concept of a Function
Linear Functions and Applications
Quadratic Functions
More Quadratic Functions and Applications
Transformations of Some Basic Curves
Combining Functions
Direct and Inverse Variation
Chapter 8 Summary
Chapter 8 Review Problem Set
Chapter 8 Test
Polynomial and Rational Functions
Synthetic Division
Remainder and Factor Theorems
Polynomial Equations
Graphing Polynomial Functions
Graphing Rational Functions
More on Graphing Rational Functions
Chapter 9 Summary
Chapter 9 Review Problem Set
Chapter 9 Test
Exponential and Logarithmic Functions
Exponents and Exponential Functions
Applications of Exponential Functions
Inverse Functions
Logarithmic Functions
Exponential Equations, Logarithmic Equations, and Problem Solving
Chapter 10 Summary
Chapter 10 Review Problem Set
Chapter 10 Test
Cumulative Review Problem Set (Chapters 1-10)
Systems of Equations
Systems of Two Linear Equations in Two Variables
Systems of Three Linear Equations in Three Variables
Matrix Approach to Solving Linear Systems
Cramer's Rule
Partial Fractions (optional)
Chapter 11 Summary
Chapter 11 Review Problem Set
Chapter 11 Test
Algebra of Matrices
Algebra of Matrices
Multiplicative Inverses
Systems of Linear Inequalities: Linear Programming
Chapter 12 Summary
Chapter 12 Review Problem Set
Chapter 12 Test
Conic Sections
Systems Involving Nonlinear Equations
Chapter 13 Summary
Chapter 13 Review Problem Set
Chapter 13 Test
Sequences and Mathematical Induction
Arithmetic Sequences
Geometric Sequences
Another Look at Problem Solving
Mathematical Induction
Chapter 14 Summary
Chapter 14 Review Problem Set
Chapter 14 Test
Prime Numbers and Operations with Fractions
Binomial Theorem
Answers to Odd-Numbered Problems and All Chapter Review, Chapter Test, Cumulative Review, and Appendix A Problems
Answers to Selected Even-Numbered Problems
Index I-1
Table of Contents provided by Publisher. All Rights Reserved.

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