This is an advanced course on partial differential equations with particular emphasis on various modern approaches. Useful formulas for solutions of some important linear partial differential equations are reviewed. Study on Sobolev spaces, second-order elliptic equations and linear evolution equations are included.

CILO-1: Identify the representation formulas for solutions of some important linear partial differential equations. CILO-2: Develop a thorough understanding of the theory of Sobolev spaces and recognize that Sobolev spaces turn out to be the proper settings in which to apply ideas of functional analysis to study partial differential equations. CILO-3: Analyze existence and regularity of solutions to uniformly elliptic, second-order partial differential equations, subject to prescribed boundary conditions. CILO-4: Use energy methods to study second-order parabolic and hyperbolic equations with solutions which evolve in time from a given initial configuration.