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Explore the mathematical foundations and applications of partial differential equations through this comprehensive lecture series delivered by Giovanni Bellettini at ICTP Mathematics. Master the theoretical framework, analytical techniques, and solution methods for various types of PDEs across 30 structured lectures totaling nearly 21 hours of instruction. Develop proficiency in understanding how partial differential equations model physical phenomena, learn classification schemes for different PDE types, and acquire skills in solving boundary value problems, initial value problems, and mixed problems. Gain expertise in separation of variables, Green's functions, Fourier analysis methods, and weak solution concepts while building a solid foundation for advanced mathematical analysis and applications in physics, engineering, and other scientific disciplines.
