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MATH 648M: Advanced Analytic Methods with Applications

This Spring the Math Department offers the graduate course…. MATH 648M: Advanced Analytic Methods with Applications. TuTh 9:30-10:45am, Rm Math 0411. Website: www.math.umd.edu/~dio/courses/648M. Instructor: Prof. Dio Margetis ( dio@math.umd.edu , x 5-5455).

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MATH 648M: Advanced Analytic Methods with Applications

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  1. ThisSpring the Math Department offers the graduate course… MATH 648M: Advanced Analytic Methods with Applications TuTh 9:30-10:45am, Rm Math 0411 Website: www.math.umd.edu/~dio/courses/648M Instructor: Prof. Dio Margetis (dio@math.umd.edu, x 5-5455) FOCUS:Mathematical concepts and analytical tools used in classicalmechanics as well as quantum mechanics and quantum field theories. Applications from: fluid mechanics, elasticity, electromagnetism, atomic and particle physics. TOPICS:PART I: Green’s functions and boundary value problems in classical mechanics. Integral equations: Fredholm eqns; the Wiener-Hopf technique. Lagrangian formulation: action principle; symmetries. Perturbation theory: Born-Neumann series and extensions. FIG. 1: Temperature around a plate (red: hot, to blue: cold). This can be derived by solving a singular integral eqn. PART II: Mathematical elements of quantum mechanics. Quantum fields: Basic notions; canonical quantization; invariance properties and gauge transformations; Yang-Mills gauge field theories. Calculus of Feynman diagrams: The S-matrix; divergencies; analytical properties; high-energy asymptotics. . e- e- e- e- FIG. 2: Electron-electron elastic scattering in quantum electrodynamics: What is the total scattering cross section in the limit of high energy? UMCP Department of Mathematics

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