مخطط الموضوع
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The lessons will be held in presence and (if necessary) at distance on Google Meet at the link: https://meet.google.com/hmw-agon-ihm.
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1.1 Elementary holomorphic functions, Cauchy-Riemann equations, elementary Riemann surfaces
1.2 Complex integration, Cauchy theorem and consequences, residue calculus
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2.1 Introduction, asymptotic sequences, and elementary examples
2.2 The Luneburg-Kline asymptotic expansion; ray optics.
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3.1 Integration by parts, Watson lemma, Laplace method, stationary-phase method
3.2 The method of steepest descents (saddle-point method)
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4.1 Point source above a single interface: space waves, lateral waves, plasmon waves, Zenneck waves
4.2 Point source above a grounded slab: surface waves, leaky waves
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5.1 PEC half plane: elementary solution and Wiener-Hopf approach
5.2 Resistive half plane: Wiener-Hopf solution and uniform asymptotic evaluation of the field
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6.1 Spherical wave functions; dipole on a PEC sphere, Watson transformation, creeping waves.
6.2 Plane-wave scattering from PEC and dielectric spheres; the rainbow and the glory.