mc_intro - Intro to Monte Carlo Methods Fred Bernardin...

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Intro to Monte Carlo Methods Fred Bernardin 10.34 November 20, 2006 Cite as: Frederick Bernardin, course materials for 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2006. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Basic Aspects of MC Applications • Stochastic – i.e., some element of randomness. • Contrast with standard integration algorithms. • When is MC useful? Cite as: Frederick Bernardin, course materials for 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2006. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Problem from Friday Class • Compute an integral of p(q)f(q)dq where p(q) is a probability distribution. • You could do it by sampling {q1,q2,q3,. ..} from the distribution p(q), and then just averaging <f> ~ {f(q1)+f(q2)+. ..+f(q3)}/N and that as N gets large this average will approach the value of the desired integral. Cite as: Frederick Bernardin, course materials for 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2006. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Basic MC Application – 2d integration • Calculate value of Pi
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 10.302 taught by Professor Clarkcolton during the Fall '04 term at MIT.

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mc_intro - Intro to Monte Carlo Methods Fred Bernardin...

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