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Index
Cover
Video Content
Title Page
Copyright Page
Preface
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 an ± bn
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)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
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