Second order linear differential equations

Learning objectives

  • Discuss the equation y^{\prime\prime} + p(t) y^\prime + q(t) y = 0
    • Solutions form 2D vector space
    • Unique solution when y(0) and y^\prime(0) are specified.
  •  Solve constant coefficient equations
  • Develop computational facility with complex numbers and exponentials
  • Explore solutions of the driven equation y^{\prime\prime} + p(t) y^\prime + q(t) y = f(t)
    • frequency response of damped harmonic oscillator

Before Class

In class