Study of ordinary differential equations, including modeling of physical problems and interpretation of their solutions. Standard solution methods for single first-order equations, including graphical and numerical methods. Higher-order forced linear equations with constant coefficients. Complex numbers and exponentials. Matrix methods for first-order linear systems with constant coefficients. Non-linear autonomous systems; phase plane analysis. Fourier series; Laplace transforms.
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.
For advanced undergraduate students: Observe resonance in a collection of driven, damped harmonic oscillators. Vary the driving frequency and amplitude, the damping constant, and the mass and spring constant of each resonator. Notice the long-lived transients when damping is small, and observe the phase change for resonators above and below resonance.
Subject:
Mathematics and Statistics, Science and Technology
No restrictions on your remixing, redistributing, or making derivative works.
Give credit to the author, as required.
Your remixing, redistributing, or making derivatives works comes with some
restrictions, including how it is shared.
Your redistributing comes with some restrictions. Do not remix or make
derivative works.
Copyrighted materials, available under Fair Use and the TEACH Act for US-based
educators, or other custom arrangements. Go to the resource provider to see
their individual restrictions.
