10/18/2013PHY 711 Fall 2013 -- Lecture 221 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 22: Summary of.

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PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
 = N  N matrix multiplication N = 3 matrix N = 3 matrix N = 3 matrix
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
PHY 711 Classical Mechanics and Mathematical Methods
Presentation transcript:

10/18/2013PHY 711 Fall Lecture 221 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 22: Summary of mathematical methods 1.Fourier transforms 2.Fast Fourier transforms

10/18/2013PHY 711 Fall Lecture 222

10/17/2012PHY 711 Fall Lecture 223 Use of Fourier transforms to solve wave equation

10/17/2012PHY 711 Fall Lecture 224 Use of Fourier transforms to solve wave equation -- continued

10/18/2013PHY 711 Fall Lecture 225 Fourier transforms

10/18/2013PHY 711 Fall Lecture 226

10/18/2013PHY 711 Fall Lecture 227

10/18/2013PHY 711 Fall Lecture 228

10/18/2013PHY 711 Fall Lecture 229 Fourier transform for periodic function – continued:

10/18/2013PHY 711 Fall Lecture 2210 Example:

10/18/2013PHY 711 Fall Lecture 2211

10/18/2013PHY 711 Fall Lecture 2212

10/18/2013PHY 711 Fall Lecture 2213

10/18/2013PHY 711 Fall Lecture 2214 Cooley-Tukey algorithm: J. W. Cooley and J. W. Tukey, “An algorithm for machine calculation of complex Fourier series” Math. Computation 19, (1965)

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