Course Outline: Differential Equations and Mathematical Modeling, Initial Value Problem, Separable Differential Equations, Exact Differential Equations, Linear Differential Equations, Bernoulli Equation, Homogeneous Linear Equations of Second Order, Second Order Homogeneous Equations with Constant Coefficients, Euler-Cauchy Equation, Existence and Uniqueness Theory, Non-homogeneous Equations, Solution by Undetermined Coefficients, Solution by Variation of Parameters, Higher-Order Linear Differential Equations, Higher-Order Homogeneous Equations with Constant Coefficients, and Higher-Order Non-homogeneous Equations, Vectors, Matrices, and Eigenvalues, Homogeneous Systems with Constant Coefficients, Critical Points, Criteria for Critical Points, Stability, Qualitative Methods for Nonlinear Systems, Non-homogenous Linear Systems, Laplace Transform, Inverse Transform, Transforms of Derivatives and Integrals, Differentiation and Integration of Transforms, Convolution, and Partial Fractions, System of Differential Equations.