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

"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 by the author"--

Science & Math

Botelho, Fabio Silva

Biological Sciences

CRC-Press

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.

Advanced Calculus and its Applications in Variational Quantum Mechanics and Relativity Theory

"The first part of this book reviews some key topics on multi-variable advanced calculus. The approach presented includes a detailed and rigorous study on surfaces in Rn which comprises items such as differential forms and an abstract version of the Stokes Theorem in Rn. In the conclusion of this first part, there is an introduction to Riemannian geometry, which will be used in the subsequent chapters of applications. In the second part, the book develops applications of the previous chapters, specifically on variational quantum mechanics and relativity theory. Topics such as a variational formulation for the relativistic Klein-Gordon equation, the derivation of a variational formulation for relativistic mechanics firstly through (semi)-Riemannian geometry, and in a second step, for a more general context, through fundamentals of differential geometry"--

Numerical Method Of Lines And Duality Principles Applied To Models In Physics And Engineering

Boca Raton : CRC Press, Taylor & Francis Group

The Numerical Method of Lines and Duality Principles Applied to Models in Physics and Engineering

Computers & Technology

Computer Science

This textbook introduces readers to real analysis in one and n dimensions. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real sequences and series. In turn, Part II addresses the multi-variable aspects of real analysis. Further, the book presents detailed, rigorous proofs of the implicit theorem for the vectorial case by applying the Banach fixed-point theorem and the differential forms concept to surfaces in Rn. It also provides a brief introduction to Riemannian geometry. With its rigorous, elegant proofs, this self-contained work is easy to read, making it suitable for undergraduate and beginning graduate students seeking a deeper understanding of real analysis and applications, and for all those looking for a well-founded, detailed approach to real analysis.

Real Analysis and Applications

Mathematics

Springer

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