Linear Algebra

Topic Covered:

Link to Linear Algebra:

Parametric Equations of Motion in 2 Dimensions

Basis Vectors, Vector Functions, and Calculus of Vectors

Systems of Equations

Gaussian Elimination and Determinants

Systems of Difference Equations

Matrices - Eigenvalues and Eigenvectors, Equilibriums and Stability

Markov Processes

Transition Matrices – Eigenvalues and Eigenvectors, Equilibriums and Stability

Parametric Equations of Motion in 3 Dimensions

Basis Vectors, Vector Functions, and Calculus of Vectors

Linear Regression and Correlation

Vector Dot Product and Projections

Equations of Lines and Planes in 3 Dimensions

Basis Vectors and Vector Products

Transformation of Variables for Multiple Integrals

Jacobian of Transformation

Vector Fields and Related Integrals

Vector Functions of Vector Variables

Systems of Linear Differential Equations

Matrices - Eigenvalues and Eigenvectors, Equilibriums and Stability

Linearization of a Nearly Linear System

Eigenvalues and Eigenvectors of Hessian Matrix

Boundary Value Problems

Eigenfunctions and Corresponding Eigenvalues

Linear Transformations and Mappings

Relation of Eigenvalues and Eigenvectors to Null Space and Image

Leslie Matrices

Transition Matrices – Eigenvalues and Eigenvectors, Equilibriums and Stability

Probability and Statistics

Topic Covered:

Link to Probability and Statistics:

Difference Equations

Geometric Distribution

Error Analysis

Normal Distribution

Systems of Difference Equations

Markov Processes

Integration

Probabilities as Areas Under Curves

Fundamental Theorem of Integral Calculus

Probability Density Functions Relation to Cumulative Distribution Functions

Improper Integrals

Exponential Distribution

Numerical Integration

Monte Carlo Method

Means and Moments

Expected Value and Variance

Vector Dot Product and Projections

Linear Regression and Correlation Coefficient

Optimization of Functions of Several Variables

Curve Fitting with Least Squares Method

Transition Matrices

Leslie Matrices

Discrete Versus Continuous

Point Probabilities Versus Area Under a Curve

Modeling

Simulation