Table of Contents
- Functions and Graphs
- Polynomial and Rational Functions
- Conic Sections, Parametric Equations, and Polar Coordinates
-
Vectors
- Components of a Vector
- Scalars, Vectors, and Directed Line Segments
- Vectors in terms of Fundamental Unit Vectors
- Magnitude of a 2D Vector
- Adding and Subtracting Vectors in 2D
- Vector Operations in 2D
- Graphical Operations on Vectors
- Dot Product in 2D
- The Angle between Two Vectors in the Coordinate Plane
- Scalar Projection
- Vectors in Space
- Dot Product in 3D
- Cross Product in 3D
- Angle between Two Vectors in Space
- Direction Angles and Direction Cosines
- Vector Fields
-
Complex Numbers
- Multiplying Complex Numbers
- Argand Diagram
- Operations on Complex Numbers in Polar Form
- Polar Form of Complex Numbers
- Dividing Complex Numbers
- Exponential Form of a Complex Number
- Complex Number Conjugates
- Pure Imaginary Numbers
- Modulus of a Complex Number
- Equating, Adding, and Subtracting Complex Numbers
- Counting and Probability
-
Limits and Rate of Change
- Limits from Tables and Graphs
- Limits by Direct Substitution
- Evaluating Limits Using Algebraic Techniques
- One-Sided Limits
- Properties of Limits
- Limits of Trigonometric Functions
- Limits at Infinity
- Continuity at a Point
- Classifying Discontinuities
- Definition of the Derivative
- Critical Points and Local Extrema of a Function
- Absolute Extrema
- Interpreting Graphs of Derivatives
- Graphing Using Derivatives
- Antiderivatives
- Indefinite Integrals: The Power Rule
- Riemann Sums
- Intermediate Value Theorem
- Series
