Chapter 1. Numbers
1.1 The Number Line And Field Axioms
1.2 Exercises
1.3 Order
1.4 Set Notation
1.5 Exercises
1.6 Order, The Short List
1.7 The Absolute Value
1.8 Exercises
1.9 Well Ordering And Archimedean Property
1.10 Exercises
1.11 Division Of Numbers
1.11.1 Review Of The Standard Algorithm
1.11.2 General Theory
1.12 Exercises
1.13 Rational Exponents
1.14 Completeness of R
1.15 Existence Of Roots
1.16 Exercises
1.17 Counting
1.17.1 Combinations
1.17.2 The Binomial Theorem
1.18 Exercises
1.19 Counting And Basic Probability
1.20 Exercises

Chapter 2. Functions      
2.1 Generalities
2.2 Real Functions
2.3 Cartesian Coordinates And Graphs
2.4 Exercises
2.5 Quadratic Functions
2.5.1 Maximizing And Minimizing
2.5.2 Solving Quadratic Equations
2.6 Exercises
2.7 Asymptotes
2.8 Exercises

Chapter 3. Division      
3.1 Division And Integers
3.2 Exercises
3.3 Rational Root Theorem
3.4 Exercises
3.5 Division And Polynomials
3.6 The Standard Algorithm
3.7 The Theory Of Division By Polynomials
3.8 Factoring Polynomials
3.9 Exercises
3.10 Technique Of Partial Fractions
3.11 Exercises
3.12 Theory Of Partial Fractions
3.12.1 Polynomials With Coefficients In A Field
3.12.2 Real Polynomials
3.13 Field Extensions
3.14 Exercises

Chapter 4. Sequences And Series
4.1 Basic Concepts
4.2 Finding A Formula
4.3 Exercises
4.4 Arithmetic And Geometric Sequences
4.4.1 The nth Term
4.4.2 The Sum
4.4.3 Compound Interest
4.4.4 Annuities
4.5 Exercises
4.6 The Limit Of A Sequence
4.6.1 Sequences And Completeness
4.6.2 Decimals
4.6.3 Infinite Series
4.7 Exercises

Chapter 5. Basic Geometry And Trigonometry
5.1 Similar Triangles And Pythagorean Theorem
5.2 Exercises
5.3 Distance Formula And Trigonometric Functions
5.4 Exercises
5.5 The Circular Arc Subtended By An Angle
5.6 The Length Of A Circular Arc
5.7 An Important Inequality
5.8 Exercises
5.9 The Trigonometric Functions
5.9.1 A Fundamental Identity
5.9.2 Reference Angles And Other Identities
5.10 Exercises
5.11 Some Basic Area Formulas
5.11.1 Areas Of Triangles And Parallelograms
5.11.2 The Area Of A Circular Sector
5.12 Exercises

Chapter 6. Exponential Functions And Logarithms
6.1 The Exponential Function
6.2 The Existence Of The Exponential Function
6.3 The Natural Logarithm
6.4 Another Approach
6.5 Raising A Positive Number To A Real Exponent
6.6 Applications
6.6.1 Interest Compounded Continuously
6.6.2 Exponential Growth And Decay
6.7 Logarithms
6.8 Exercises

Chapter 7. Parabolas, Ellipses, and Hyperbolas 
7.1 The Parabola
7.2 The Ellipse
7.3 The Hyperbola
7.4 Exercises

Chapter 8. Polar Coordinates And Graphs
8.1 Exercises

Chapter 9. The Complex Numbers
9.1 Polar Form Of Complex Numbers
9.2 Roots Of Complex Numbers
9.3 The Quadratic Formula
9.4 Exercises

Chapter 10. Systems Of Equations
10.1 Systems Of Equations, Geometric Interpretations
10.2 Systems Of Equations, Algebraic Procedures
10.2.1 Elementary Operations
10.2.2 Gauss Elimination
10.3 Exercises

Chapter 11. Vectors
11.1 Rn
11.2 Algebra in Rn
11.3 Geometric Meaning Of Vectors
11.4 Geometric Meaning Of Vector Addition
11.5 Distance Between Points In Rn Length Of A Vector
11.6 Meaning Of Scalar Multiplication
11.7 Lines
11.8 Exercises
11.9 Vectors And Physics
11.10 Exercises

Chapter 12. Vector Products
12.1 The Dot Product
12.2 The Significance Of The Dot Product
12.2.1 The Angle Between Two Vectors
12.2.2 Work And Projections
12.3 Exercises
12.4 The Cross Product
12.4.1 The Box Product
12.4.2 A Proof Of The Distributive Law
12.4.3 Torque
12.5 Exercises