Schaum's Outline of College Algebra, Third Edition | Schaum's Outline

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Schaum's Outline of College Algebra, Third Edition

Schaum's Outline of College Algebra, Third Edition

Authors: Murray Spiegel and Robert Moyer

Published: August 2009

eISBN: 9780071702638 0071702636 | ISBN: 9780071635394

Contents

Chapter 1 Fundamental Operations with Numbers

1.1 Four Operations

1.2 System of Real Numbers

1.3 Graphical Representation of Real Numbers

1.4 Properties of Addition and Multiplication of Real Numbers

1.5 Rules of Signs

1.6 Exponents and Powers

1.7 Operations with Fractions

Chapter 2 Fundamental Operations with Algebraic Expressions

2.1 Algebraic Expressions

2.2 Terms

2.3 Degree

2.4 Grouping

2.5 Computation with Algebraic Expressions

Chapter 3 Properties of Numbers

3.1 Sets of Numbers

3.2 Properties

3.3 Additional Properties

Chapter 4 Special Products

4.1 Special Products

4.2 Products Yielding Answers of the Form a[sup(n)]±b[sup(n)]

Chapter 5 Factoring

5.1 Factoring

5.2 Factorization Procedures

5.3 Greatest Common Factor

5.4 Least Common Multiple

Chapter 6 Fractions

6.1 Rational Algebraic Fractions

6.2 Operations with Algebraic Fractions

6.3 Complex Fractions

Chapter 7 Exponents

7.1 Positive Integral Exponent

7.2 Negative Integral Exponent

7.3 Roots

7.4 Rational Exponents

7.5 General Laws of Exponents

7.6 Scientific Notation

Chapter 8 Radicals

8.1 Radical Expressions

8.2 Laws for Radicals

8.3 Simplifying Radicals

8.4 Operations with Radicals

8.5 Rationalizing Binomial Denominators

Chapter 9 Simple Operations with Complex Numbers

9.1 Complex Numbers

9.2 Graphical Representation of Complex Numbers

9.3 Algebraic Operations with Complex Numbers

Chapter 10 Equations in General

10.1 Equations

10.2 Operations Used in Transforming Equations

10.3 Equivalent Equations

10.4 Formulas

10.5 Polynomial Equations

Chapter 11 Ratio, Proportion, and Variation

11.1 Ratio

11.2 Proportion

11.3 Variation

11.4 Unit Price

11.5 Best Buy

Chapter 12 Functions and Graphs

12.1 Variables

12.2 Relations

12.3 Functions

12.4 Function Notation

12.5 Rectangular Coordinate System

12.6 Function of Two Variables

12.7 Symmetry

12.8 Shifts

12.9 Scaling

12.10 Using a Graphing Calculator

Chapter 13 Linear Equations in One Variable

13.1 Linear Equations

13.2 Literal Equations

13.3 Word Problems

Chapter 14 Equations of Lines

14.1 Slope of a Line

14.2 Parallel and Perpendicular Lines

14.3 Slope–Intercept form of Equation of a Line

14.4 Slope–Point Form of Equation of a Line

14.5 Two-point Form of Equation of a Line

14.6 Intercept Form of Equation of a Line

Chapter 15 Simultaneous Linear Equations

15.1 Systems of Two Linear Equations

15.2 Systems of Three Linear Equations

Chapter 16 Quadratic Equations in One Variable

16.1 Quadratic Equations

16.2 Methods of Solving Quadratic Equations

16.3 Sum and Product of the Roots

16.4 Nature of the Roots

16.5 Radical Equations

16.6 Quadratic-type Equations

Chapter 17 Conic Sections

17.1 General Quadratic Equations

17.2 Conic Sections

17.3 Circles

17.4 Parabolas

17.5 Ellipses

17.6 Hyperbolas

17.7 Graphing Conic Sections with a Calculator

Chapter 18 Systems of Equations Involving Quadratics

18.1 Graphical Solution

18.2 Algebraic Solution

Chapter 19 Inequalities

19.1 Definitions

19.2 Principles of Inequalities

19.3 Absolute Value Inequalities

19.4 Higher Degree Inequalities

19.5 Linear Inequalities in Two Variables

19.6 Systems of Linear Inequalities

19.7 Linear Programming

Chapter 20 Polynomial Functions

20.1 Polynomial Equations

20.2 Zeros of Polynomial Equations

20.3 Solving Polynomial Equations

20.4 Approximating Real Zeros

Chapter 21 Rational Functions

21.1 Rational Functions

21.2 Vertical Asymptotes

21.3 Horizontal Asymptotes

21.4 Graphing Rational Functions

21.5 Graphing Rational Functions using a Graphing Calculator

Chapter 22 Sequences and Series

22.1 Sequences

22.2 Arithmetic Sequences

22.3 Geometric Sequences

22.4 Infinite Geometric Series

22.5 Harmonic Sequences

22.6 Means

Chapter 23 Logarithms

23.1 Definition of a Logarithm

23.2 Laws of Logarithms

23.3 Common Logarithms

23.4 Using a Common Logarithm Table

23.5 Natural Logarithms

23.6 Using a Natural Logarithm Table

23.7 Finding Logarithms Using a Calculator

Chapter 24 Applications of Logarithms and Exponents

24.1 Introduction

24.2 Simple Interest

24.3 Compound Interest

24.4 Applications of Logarithms

24.5 Applications of Exponents

Chapter 25 Permutations and Combinations

25.1 Fundamental Counting Principle

25.2 Permutations

25.3 Combinations

25.4 Using a Calculator

Chapter 26 The Binomial Theorem

26.1 Combinatorial Notation

26.2 Expansion of (a+x)[sup(n)]

Chapter 27 Probability

27.1 Simple Probability

27.2 Compound Probability

27.3 Mathematical Expectation

27.4 Binomial Probability

27.5 Conditional Probability

Chapter 28 Determinants

28.1 Determinants of Second Order

28.2 Cramer's Rule

28.3 Determinants of Third Order

28.4 Determinants of Order n

28.5 Properties of Determinants

28.6 Minors

28.7 Value of a Determinant of Order n

28.8 Cramer's Rule for Determinants of Order n

28.9 Homogeneous Linear Equations

Chapter 29 Matrices

29.1 Definition of a Matrix

29.2 Operations With Matrices

29.3 Elementary Row Operations

29.4 Inverse of a Matrix

29.5 Matrix Equations

29.6 Matrix Solution of a System of Equations

Chapter 30 Mathematical Induction

30.1 Principle of Mathematical Induction

30.2 Proof by Mathematical Induction

Chapter 31 Partial Fractions

31.1 Rational Fractions

31.2 Proper Fractions

31.3 Partial Fractions

31.4 Identically Equal Polynomials

31.5 Fundamental Theorem

31.6 Finding the Partial Fraction Decomposition

Appendix A: Table of Common Logarithms

Appendix B: Table of Natural Logarithms

Index