Differential equation, Initial-Value problem, Solution of a differential equation, Linear differential equation, Separable variables, Exact equations, Linear equations, Applications on first order ODE. Differential equation of higher order, Linear dependence and linear independence, Wronskian, Reduction of order, Homogeneous equation, Undetermined coefficients, Variation of parameters, Application of Higher order ODE, Vector spaces, matrices, systems of linear equations, determinants, and inner products. Applications may include differential equations, and models in Chemistry.

Probability Axioms, Conditional Probability and Bayes Theorem, Random Variables and their Independence, Moment Generating Function, Conditional Expectation, Discrete and Continuous Probability Distribution, Covariance, Functions of the Random Variables, Order Statistics , Central limit Theorem.