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College Algebra（大学代数学）

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LI Lanqing (li_lanqing@founder.co.jp)

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Chapter 0 Introductory Material

Introductory Material
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Chapter 1 Prerequisites

Introduction
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1.1 Real Numbers: Algebra Essentials
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1.2 Exponents and Scientific Notation
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1.3 Radicals and Rational Exponents
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1.4 Polynomials
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1.5 Factoring Polynomials
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1.6 Rational Expressions
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Chapter 1 Review
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Chapter 2 Equations and Inequalities

Introduction
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2.1 The Rectangular Coordinate Systems and Graphs
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2.2 Linear Equations in One Variable
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2.3 Models and Applications
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2.4 Complex Numbers
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2.5 Quadratic Equations
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2.6 Other Types of Equations
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2.7 Linear Inequalities and Absolute Value Inequalities
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Chapter 2 Review
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Chapter 3 Functions

Introduction
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3.1 Functions and Function Notation
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3.2 Domain and Range
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3.3 Rates of Change and Behavior of Graphs
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3.4 Composition of Functions
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3.5 Transformation of Functions
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3.6 Absolute Value Functions
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3.7 Inverse Functions
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Chapter 3 Review
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Chapter 4 Linear Functions

Introduction
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4.1 Linear Functions
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4.2 Modeling with Linear Functions
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4.3 Fitting Linear Models to Data
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Chapter 4 Review
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Chapter 5 Polynomial and Rational Functions

Introduction
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5.1 Quadratic Functions
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5.2 Power Functions and Polynomial Functions
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5.3 Graphs of Polynomial Functions
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5.4 Dividing Polynomials
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5.5 Zeros of Polynomial Functions
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5.6 Rational Functions
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5.7 Inverses and Radical Functions
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5.8 Modeling Using Variation
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Chapter 5 Review
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Chapter 6 Exponential and Logarithmic Functions

Introduction
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6.1 Exponential Functions
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6.2 Graphs of Exponential Functions
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6.3 Logarithmic Functions
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6.4 Graphs of Logarithmic Functions
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6.5 Logarithmic Properties
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6.6 Exponential and Logarithmic Equations
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6.7 Exponential and Logarithmic Models
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6.8 Fitting Exponential Models to Data
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Chapter 6 Review
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Chapter 7 Systems of Equations and Inequalities

Introduction
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7.1 Systems of Linear Equations: Two Variables
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7.2 Systems of Linear Equations: Three Variables
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7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
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7.4 Partial Fractions
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7.5 Matrices and Matrix Operations
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7.6 Solving Systems with Gaussian Elimination
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7.7 Solving Systems with Inverses
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7.8 Solving Systems with Cramer's Rule
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Chapter 7 Review
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Chapter 8 Analytic Geometry

Introduction
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8.1 The Ellipse
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8.2 The Hyperbola
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8.3 The Parabola
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8.4 Rotation of Axis
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8.5 Conic Sections in Polar Coordinates
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Chapter 8 Review
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Chapter 9 Sequences, Probability and Counting Theory

Introduction
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9.1 Sequences and Their Notation
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9.2 Arithmetic Sequences
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9.3 Geometric Sequences
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9.4 Series and Their Notations
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9.5 Counting Principles
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9.6 Binomial Theorem
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9.7 Probability
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Chapter 9 Review
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