This two-volume textbook offers finished assurance of partial differential equations, spanning elliptic, parabolic, and hyperbolic varieties in and several other variables. during this moment quantity, precise emphasis is put on practical analytic equipment and purposes to differential geometry. the next issues are taken care of: solvability of operator equations in Banach spaces linear operators in Hilbert areas and spectral conception Schauder's thought of linear elliptic differential equations susceptible options of differential equations nonlinear partial differential equations and characteristicsnonlinear elliptic systemsboundary worth difficulties from differential geometryThis new moment variation of this quantity has been completely revised and a brand new bankruptcy on boundary price difficulties from differential geometry has been added.In the 1st quantity, partial differential equations through quintessential representations are taken care of in a classical way.This textbook could be of specific use to graduate and postgraduate scholars attracted to this box and should be of curiosity to complex undergraduate scholars. it may well even be used for self sustaining study.