lec12_10062006 - 10.34 Numerical Methods Applied to...

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10.34, Numerical Methods Applied to Chemical Engineering Professor William H. Green Lecture #12: Ordinary Differential Equation Initial Value Problems (ODE-IVPs) and Numerical Integration. From Last Lecture: Singular Value Decomposition S observed ( λ n ,t k ) = Σ x i (t k )A i ( λ n ) + noise SVD Σσ i U i (t k )V i T ( λ n ) Fixed in time. Amplitude changes with wavelength For a system where only one chemical absorbs light, expect one singular value to be bigger. The rest of the singular values relate to noise. Look in Beer’s textbook for exact notation. ODE-IVP: Numerical Integration dx /dt = F (x ) ODE F = ma d 2 x /dt 2 = F (x ,dx /dt)/m dv /dt = F/m dx /dt = v () = v m v x F x V dt d , so setting x 1 =v and x 2 =x gives ( ) () x x m x F x x dt d F 1 2 1 = = g (x , dx / dt ) = 0 D A E Î differential algebraic equations Boundary Conditions: Initial Value Problems (IVPs)
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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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lec12_10062006 - 10.34 Numerical Methods Applied to...

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