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Computational Calculus, or, How I Stopped Worrying and Learned to Love Differential Equations

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Published on Mar 8, 2016

This is an introduction to the MMCC (mathematical modeling and computational calculus) series of videos. Note: there are no prerequisites for this series. Computational calculus is easy, trust me.

Here's the thing - physics and engineering are based on differential equations - the physical laws, e.g. F=MA, are differential equations, and the process models are written as differential equations. The problem is that differential equations are mostly impossible to solve. The worlds first differential equation was Newton's equation for the acceleration of a falling object, A = G*M/R*R, taught in high school physics, it is unsolvable. Physics and engineering are difficult because most differential equations are impossible to solve.

Of course the university doesn't tell you differential equations are unsolvable. They let you flail around for years taking courses in integral, differential, and multivariable calculus, then a course in differential equations, followed by a course in Fourier analysis and the Laplace transform, and finally a course in linear systems theory. And you still can't compute the trajectory of a falling apple.

OTOH, it takes us 1 or 2 vids to compute a falling apple's trajectory, and then were off to the races ....

This vid - an overview of the MMCC I series of vids: the use of computational calculus to model and analyze physical systems including falling objects, orbits, rocket trajectories, the Apollo mission, the Juno probe, electrical circuits, rigid body dynamics, airplane simulation, rocket guidance, and robot control. Plus an overview of the MMCC II series on heat transfer, the wave equation, stress and strain in materials, fluid dynamics, and electrodynamics !

Class notes, including complete MATLAB programs and links to MATLAB, OCTAVE, and FREEMAT apps, at
http://berkeleyscience.com/classnotes

Synopsis of MMCC I at
http://berkeleyscience.com/mmcc.htm

Synopsis of MMCC II at
http://berkeleyscience.com/mmcc2.htm

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