Table of Contents
-
Integration
- Antiderivatives
- Indefinite Integrals: The Power Rule
- Applications of Indefinite Integration
- Indefinite Integrals: Exponential and Reciprocal Functions
- Indefinite Integrals: Trigonometric Functions
- Integration by Substitution: Indefinite Integrals
- Integration by Partial Fractions with Linear Factors
- Integrals Resulting in Inverse Trigonometric Functions
-
Definite Integration and Its Applications
- Definite Integrals as Limits of Riemann Sums
- The Fundamental Theorem of Calculus: Evaluating Definite Integrals
- Properties of Definite Integrals
- Area between a Curve and a Line
- Area between Curves
- Volumes of Solids of Revolution
- Rectilinear Motion and Integration
- Basics of Differential Equations
- Separable Differential Equations
-
Vectors
- Scalars, Vectors, and Directed Line Segments
- Vectors in terms of Fundamental Unit Vectors
- Magnitude of a 2D Vector
- Polar Form of a Vector
- Adding and Subtracting Vectors in 2D
- Vector Operations in 2D
- Graphical Operations on Vectors
- Vector Applications
- Dot Product in 2D
- Vectors in Space
- Vector Operations in 3D
- Magnitude of a Vector in 3D
- Scalar Multiplication and Unit Vectors
- Dot Product in 3D
- Angle between Two Vectors in Space
- Direction Angles and Direction Cosines
-
Complex Numbers
- Introduction to Complex Numbers
- Equating, Adding, and Subtracting Complex Numbers
- Multiplying Complex Numbers
- Complex Number Conjugates
- Dividing Complex Numbers
- Solving Quadratic Equations with Complex Roots
- Argand Diagram
- Modulus of a Complex Number
- Polar Form of Complex Numbers
- Operations on Complex Numbers in Polar Form
- De Moivre’s Theorem
- The 𝑛th Roots of Unity
- Arbitrary Roots of Complex Numbers
- Cube Roots of Unity
- Probability Distributions