First Order Differential Equations: Linear Equations, Separable Equations, Exact Equations, Equilibrium Solutions, Modeling Problems.

Second Order Differential Equations: Homogeneous and Nonhomogeneous Second Order Differential Equations, Fundamental Set of Solutions, Undetermined Coefficients, Variation of Parameters, Mechanical Vibrations

Laplace Transforms: Definition, Inverse Transforms, Step Functions, Heaviside Functions, Dirac-Delta Function, Solving IVP's, Nonhomogeneous IVP, Nonconstant Coefficient IVP, Convolution Integral.

Systems of Differential Equations: Matrix Form, Eigenvalues/Eigenvectors, Phase Plane, Nonhomogeneous Systems, Laplace Transforms.

Series Solutions: Series Solutions, Euler Differential Equations.

Higher Order Differential Equations: nth order differential equations, Undetermined Coefficients, Variation of Parameters, 3 x 3 Systems of Differential Equations.

Boundary Value Problems & Fourier Series: Boundary Value Problems, Eigenvalues and Eigenfunctions, Orthogonal Functions, Fourier Sine Series, Fourier Cosine Series, Fourier Series.

Parital Differential Equations: Heat Equation, Wave Equation, Laplace's Equation, Separation of Variables.

These notes assume no prior knowledge of differential equations. A good grasp of Calculus is required however. This includes a working knowledge of differentiation and integration.