Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering - Botelho, Fabio Silva (Milton : Taylor & Francis Group, 2020)
The book discusses basic concepts of functional analysis, measure and integration theory, calculus of variations and duality and its 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 to applied mathematicians and graduate students in applied mathematics. Physicists, engineers and researchers in related fields will also find the book useful in providing a mathematical background applicable to their respective professional areas.
6.7.1 The spectral theorem using Cayley transform -- 7. Basic Results on Measure and Integration -- 7.1 Basic concepts -- 7.2 Simple functions -- 7.3 Measures -- 7.4 Integration of simple functions -- 7.5 Signed measures -- 7.6 The Radon-Nikodym theorem -- 7.7 Outer measure and measurability -- 7.8 Fubini's theorem -- 7.8.1 Product measures -- 8. The Lebesgue Measure in Rn -- 8.1 Introduction -- 8.2 Properties of the outer measure -- 8.3 The Lebesgue measure -- 8.4 Outer and inner approximations of Lebesgue measurable sets -- 8.5 Some other properties of measurable sets
8.6 Lebesgue measurable functions
OCLC-licensed vendor bibliographic record.
Keywords: Calculus of variations; Functional analysis; MATHEMATICS -- Functional Analysis; SCIENCE -- Mathematical Physics; MATHEMATICS -- General