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

The book discusses functional analysis, measure and integration theory, calculus of variations and duality, and their applications to variational problems of non-convex nature. It also covers numerical methods for these problems and recent research on Riemannian geometry applied to Quantum Mechanics and Relativity.

Format: Paperback / softback
Length: 588 pages
Publication date: 30 May 2022
Publisher: Taylor & Francis Ltd

The book delves into the fundamental principles of functional analysis, measure and integration theory, calculus of variations, and duality, with a focus on their applications to variational problems of non-convex nature. These problems encompass a wide range of topics, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism, and more. To address these challenges, numerical methods have been developed using the generalized method of lines, including matrix finite dimensional approximations. These methods have proven invaluable in modeling and solving complex problems in flight mechanics and the Navier-Stokes system in fluid mechanics.

Furthermore, the book concludes with a comprehensive review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity. This interdisciplinary approach sheds light on the connections between classical and quantum physics, offering new insights into the fundamental nature of spacetime and matter.

Overall, the book is a valuable resource for applied mathematicians, graduate students in applied mathematics, physicists, engineers, and researchers in related fields. It provides a comprehensive and up-to-date introduction to the mathematical techniques and applications relevant to modern physics and engineering.

Weight: 1090g
Dimension: 254 x 178 (mm)
ISBN-13: 9780367510039