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10/15/2015PHY 711 Fall 2014 -- 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: "10/15/2015PHY 711 Fall 2014 -- 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 10/15/2015PHY 711 Fall 2014 -- Lecture 221 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 22: Summary of some mathematical tools 1.Contour integration 2.Fourier transforms 3.Fast Fourier transforms

2 10/15/2015PHY 711 Fall 2014 -- Lecture 222

3 10/15/2015PHY 711 Fall 2014 -- Lecture 223

4 10/15/2015PHY 711 Fall 2014 -- Lecture 224

5 10/15/2015PHY 711 Fall 2014 -- Lecture 225

6 10/15/2015PHY 711 Fall 2014 -- Lecture 226 Example Re(z) Im(z)

7 10/15/2015PHY 711 Fall 2014 -- Lecture 227 Example -- continued Re(z) Im(z)

8 10/15/2015PHY 711 Fall 2014 -- Lecture 228 Example -- continued Re(z) Im(z) x’

9 10/15/2015PHY 711 Fall 2014 -- Lecture 229 Example -- continued Kramers-Kronig relationship

10 10/15/2015PHY 711 Fall 2014 -- Lecture 2210

11 10/15/2015PHY 711 Fall 2014 -- Lecture 2211 Example: Re(z) Im(z)

12 10/15/2015PHY 711 Fall 2014 -- Lecture 2212 Contour integral for homework:

13 10/15/2015PHY 711 Fall 2014 -- Lecture 2213 Fourier transforms

14 10/15/2015PHY 711 Fall 2014 -- Lecture 2214 Note: The location of the 2  factor varies among texts.

15 10/15/2015PHY 711 Fall 2014 -- Lecture 2215

16 10/15/2015PHY 711 Fall 2014 -- Lecture 2216 Use of Fourier transforms to solve wave equation

17 10/15/2015PHY 711 Fall 2014 -- Lecture 2217 Use of Fourier transforms to solve wave equation -- continued

18 10/15/2015PHY 711 Fall 2014 -- Lecture 2218

19 10/15/2015PHY 711 Fall 2014 -- Lecture 2219

20 10/15/2015PHY 711 Fall 2014 -- Lecture 2220 Example:

21 10/15/2015PHY 711 Fall 2014 -- Lecture 2221 Example: f(t) F(  )

22 10/15/2015PHY 711 Fall 2014 -- Lecture 2222 F(  ) =-M =M

23 10/15/2015PHY 711 Fall 2014 -- Lecture 2223

24 10/15/2015PHY 711 Fall 2014 -- Lecture 2224

25 10/15/2015PHY 711 Fall 2014 -- Lecture 2225

26 10/15/2015PHY 711 Fall 2014 -- Lecture 2226 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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