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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 some mathematical tools 1.Contour integration 2.Fourier transforms 3.Fast Fourier transforms
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10/15/2015PHY 711 Fall 2014 -- Lecture 222
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10/15/2015PHY 711 Fall 2014 -- Lecture 223
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10/15/2015PHY 711 Fall 2014 -- Lecture 224
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10/15/2015PHY 711 Fall 2014 -- Lecture 225
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10/15/2015PHY 711 Fall 2014 -- Lecture 226 Example Re(z) Im(z)
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10/15/2015PHY 711 Fall 2014 -- Lecture 227 Example -- continued Re(z) Im(z)
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10/15/2015PHY 711 Fall 2014 -- Lecture 228 Example -- continued Re(z) Im(z) x’
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10/15/2015PHY 711 Fall 2014 -- Lecture 229 Example -- continued Kramers-Kronig relationship
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10/15/2015PHY 711 Fall 2014 -- Lecture 2210
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10/15/2015PHY 711 Fall 2014 -- Lecture 2211 Example: Re(z) Im(z)
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10/15/2015PHY 711 Fall 2014 -- Lecture 2212 Contour integral for homework:
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10/15/2015PHY 711 Fall 2014 -- Lecture 2213 Fourier transforms
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10/15/2015PHY 711 Fall 2014 -- Lecture 2214 Note: The location of the 2 factor varies among texts.
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10/15/2015PHY 711 Fall 2014 -- Lecture 2215
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10/15/2015PHY 711 Fall 2014 -- Lecture 2216 Use of Fourier transforms to solve wave equation
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10/15/2015PHY 711 Fall 2014 -- Lecture 2217 Use of Fourier transforms to solve wave equation -- continued
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10/15/2015PHY 711 Fall 2014 -- Lecture 2218
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10/15/2015PHY 711 Fall 2014 -- Lecture 2219
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10/15/2015PHY 711 Fall 2014 -- Lecture 2220 Example:
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10/15/2015PHY 711 Fall 2014 -- Lecture 2221 Example: f(t) F( )
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10/15/2015PHY 711 Fall 2014 -- Lecture 2222 F( ) =-M =M
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10/15/2015PHY 711 Fall 2014 -- Lecture 2223
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10/15/2015PHY 711 Fall 2014 -- Lecture 2224
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10/15/2015PHY 711 Fall 2014 -- Lecture 2225
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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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