Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering

Functional analysis and the calculus of variations deals with the real analysis formalism for functionals and operators defined on spaces of infinite dimension. In particular, the calculus of variations generalizes and extends the standard differential and integral calculus theory for n real variables to infinite dimensional spaces of real functions. The book discusses the basic concepts of functional analysis, measure and integration theory, calculus of variations and duality aiming applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism and others. Numerical Methods for such and similar problems, such as models in flight mechanics and the Navier-Stokes system in fluid mechanics have been developed through the generalized method of lines, including their matrix finite dimensional approximations. It concludes with a review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity. The book will be of interest mainly for applied mathematicians and graduate students in applied mathematics. Physicists, engineers and researchers in related fields may also find the book an interesting source of advanced mathematical background applicable to their respective professional areas.