Calculus
Precalculus
- Square Root
- Absolute Values
- Quadratic Functions
- Complex Numbers
- Complex Plane
- De Moivre’s Theorem
- Roots of a Complex Number
- Euler’s Formula
- Polar Coordinates
- Spherical Polar Coordinates
- Polar Rectangles
- Movement of Graphs
Limits
- The number “e” as a Limit
- Squeeze theorem
- Important Limit Values
- L’Hospital’s Rule
- Continuity
- Ratio Test
Functions
- Even / Odd Functions
- Periodic Functions
- Composite Functions
- One-to-One Function
- Inverse Functions
- Exponential Functions
- Logarithmic Functions
- Natural Logarithms
- Trigonometric Functions
- Trigonometric Functions / Applications to Triangles
- Inverse Trigonometric Functions
- Hyperbolic Functions
- Inverse Hyperbolic Functions
- Parametric Equations
- Implicit Functions
Taylor Series Expansion
- Binomial Theorem / Multinomial Theorem
- Taylor and Maclaurin Series
- Proof of Taylor Series Expansion
- Approximating Functions by Taylor Polynomials
Space Vectors
- Dot Products
- Cross Products
- Length of The Cross Products
- Geometric Interpretation of Cross Products
- Scalar Triple Products
- Vector Projections
Derivative
- Theorems of Derivative
- Tangent and Normal Lines
- Differentiation Formulas (Review)
- Implicit Differentiation
- General Leibniz Rule
Integrals
- Integration Formulas
Techniques of Integration
- Integration by Parts
- Trigonometric Integrals
- Integration of Rational Functions
- Substitution Rule : involving Irrational Functions / Trigonometric Functions / \(\mathrm{e}^{x}\)
- Trigonometric Substitution
Applications of Integration
- Arc Length
- Volume
- Area of a Surface of Revolution
Partial Derivatives
Linear Algebra
Matrix
- Inverse Matrix
- Transposed Matrix
- Symmetric Matrix
- Alternating Matrix
- Diagonal Matrix
- Orthogonal matrix
Determinant
- Determinant
- Permutation
- Vandermonde Matrix
Linear System
- Solving a Linear System
- Row Reduction Algorithm
- Cramer’s Rule
Inner Product
- Inner Product
- Length of Inner Product
- Orthogonality
- Projection
- Gram-Schmidt Process
Diagonalization
- Diagonal Matrix
- Basis
- Linear Transformation
- Eigen values and Eigenvectors
- Diagonalization
Probability
Permutation / Combinations
- Permutations
- Combinations
- Binomial Theorem
Sample Space
- Independent
- Conditional Probability
- Bay’s Theorem
Probability Functions
- Expectations
- Variance and Standard Deviation
- Covariance
- Correlation Coefficient
- Marginal Probability Functions
- Joint Probability Functions
- Moment Generating Functions
- Characteristic Functions
Distributions
- Binomial Distribution
- Normal Distribution
- Log-Normal Distribution
- Poisson Distribution
- Multinomial Distribution
- Uniform Distribution
- Cauchy Distribution
- Exponential Distribution
- \(\chi^{2}\) Distribution
- t-Distribution
- F-Distribution