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This moment within the sequence of 3 volumes builds upon the fundamental conception of linear PDE given in quantity 1, and pursues extra complex subject matters. Analytical instruments brought right here comprise pseudodifferential operators, the useful research of self-adjoint operators, and Wiener degree. The publication additionally develops uncomplicated differential geometrical strategies, targeted approximately curvature. issues lined comprise spectral idea of elliptic differential operators, the idea of scattering of waves via hindrances, index concept for Dirac operators, and Brownian movement and diffusion.