Differential Equations

03272017, 11:46 PM
Post: #17




RE: Differential Equations
(03272017 07:27 PM)ttw Wrote: The first derivative of the distance is the velocity.I got my first exposure to real calculus as a freshman Civil Engineering student. During an early practice session, we were shown the basic of stress analysis, with the example of a uniform, prismatic, horizontal beam, supported at both ends. The prof then started defining the beam's weight as a function of distance along the beam (not weight, of course, but density, but you get the idea). Being a uniform prismatic beam, this function is constant. Then comes the first integral, which gives you shear stress. The second gives you torque. The third gives you bend. The fourth gives you sag. Any loads are added to the weight function; the specifics of the supports are expressed as boundary conditions. The whole thing was more complicated than this, of course. The prof didn't just say "integrate shear stress and poof, you get torque" – he worked it all out on the blackboard with diagrams and infinitisemals. And it was extremely cool to see calculus come to life like that, with an extremely tangible realworld application. 

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