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A spring system reacts to be shaken by vibration. When the input frequency is near a natural mode of the system, the amplitude is great. This can be understood in the frequency range with the Laplace transformation and its pole diagram. (Image Courtesy Hu Hohn and Prof. Haynes Miller.)
prof. Haynes Miller
prof. Arthur Mattuck
How to taught
Lecture notes, student work
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Differential equations are the language in which the natural laws are expressed. The understanding of real estate of differential equations solutions is fundamental to most of contemporary science and engineering. Ordinary differential equations (ODE) deal with functions of a variable that can often be considered as a time.