Ordinary differential equations

• How to Calculate Barometric Pressure at an Altitude
  Use hydrostatic balance and the ideal-gas law to derive the exponential barometric formula and estimate pressure at a chosen altitude.
• How to Derive the Hermite Polynomial Derivative Relation
  Differentiate the physicists’ Hermite equation to show H_n' solves the degree-(n−1) equation, then compare leading coefficients to get H_n'=2nH_{n−1}.
• How to Use Variation of Parameters for a 3×3 System
  Use a fundamental matrix to solve a nonhomogeneous 3×3 linear ODE system by variation of parameters, with a worked example.