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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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Presentation on theme: "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."— Presentation transcript:

1 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 mathematical methods 1.Fourier transforms 2.Fast Fourier transforms

2 10/18/2013PHY 711 Fall 2013 -- Lecture 222

3 10/17/2012PHY 711 Fall 2012 -- Lecture 223 Use of Fourier transforms to solve wave equation

4 10/17/2012PHY 711 Fall 2012 -- Lecture 224 Use of Fourier transforms to solve wave equation -- continued

5 10/18/2013PHY 711 Fall 2013 -- Lecture 225 Fourier transforms

6 10/18/2013PHY 711 Fall 2013 -- Lecture 226

7 10/18/2013PHY 711 Fall 2013 -- Lecture 227

8 10/18/2013PHY 711 Fall 2013 -- Lecture 228

9 10/18/2013PHY 711 Fall 2013 -- Lecture 229 Fourier transform for periodic function – continued:

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

11 10/18/2013PHY 711 Fall 2013 -- Lecture 2211

12 10/18/2013PHY 711 Fall 2013 -- Lecture 2212

13 10/18/2013PHY 711 Fall 2013 -- Lecture 2213

14 10/18/2013PHY 711 Fall 2013 -- Lecture 2214 Cooley-Tukey algorithm: J. W. Cooley and J. W. Tukey, “An algorithm for machine calculation of complex Fourier series” Math. Computation 19, 297-301 (1965)

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