First Order Differential Equations Linear Equations Separable Equations Equilibria and the Phase Line Bifurcations Bernoulli Equations Riccati Equations Homogeneous Equations Exact and Non-Exact Equations Some Applications Newton's Law of Cooling Population Dynamics Numerical Technique: Euler's Method Systems of Differential Equations Decoupled Systems Euler's Method for Systems Linear Systems Eigenvalues and Eigenvectors Technique Real Eigenvalues Repeated Eigenvalues Complex Eigenvalues Second Order Differential Equations Homogenous with Constant Coefficients Harmonic Oscillator: Spring-Mass System Nonlinear Systems: Nullclines Equilibrium Point Analysis: Linearization Technique Laplace Transform Laplace Transform of simple functions Laplace Transform of step or discontinuous functions Inverse Laplace Transform of simple functions Inverse Laplace Transform of step or discontinuous functions Application to Differential Equations Table of Laplace Transform