The primary goal is to utilize and apply fundamental notions, abstractions, and principles of functional analysis towards solving concrete mathematical problems arising in engineering and natural sciences. In addition we aim at strengthening students' analytical, logical reasoning, and problem solving abilities.

• Identify functional analytic abstractions in statements of concrete model problems
• Interpret model problems in functional analytic terms and formally verify prerequisites for such interpretations
• Utilize and apply fundamental functional analytic principles towards analyzing and solving model problems
• Interpret certain computational algorithms in functional analytic terms
• Follow and apply logical strategies of formal mathematical arguments
• Establish the validity mathematical statements about models by constructing and providing formal arguments

This is a topical course and its content may vary from one year to another. Representative topics include: calculus of variations, frames, harmonic analysis, integral and partial differential equations, inverse problems, numerical functional analysis, PDE-constrained optimization, wavelet and multiresolution analysis. Please contact course responsible for more information.

In Spring 2013, the course theme is: functional analytic methods for integral and/or partial differential equations. Some specific keywords include: compact sets and operators; Sobolev spaces; fixed point theorems; Galerkin method.