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Bibliothèque des sciences et technologies - Learning Center Pasteur

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Les Bibliothèques et Learning Centers de l'Université catholique de Louvain

Bibliothèque des sciences et technologies - Learning Center Pasteur

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14 April 2025

Accès réservé aux membres UCLouvain.  Accès à distance ?

Carathéodory, C. (2024)

Calculus of Variations and Partial Differential Equations of First Order: Second Edition. 

1st ed. Providence: American Mathematical Society (AMS Chelsea Publishing Series, v. 318).

 

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"In this second English edition of Carathéodory's famous work (originally published in German), the two volumes of the first edition have been combined into one (with a combination of the two indexes into a single index). There is a deep and fundamental relationship between the differential equations that occur in the calculus of variations and partial differential equations of the first order: in particular, to each such partial differential equation there correspond variational problems. This basic fact forms the rationale for Carathéodory's masterpiece. Includes a Guide to the Literature and an Index."
 
Morrey Jr., C.B. (2008) 

Multiple Integrals in the Calculus of Variations. 

Berlin, Heidelberg: Springer Berlin / Heidelberg (Classics in Mathematics Ser).

 

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"From the reviews:'…the book contains a wealth of material essential to the researcher concerned with multiple integral variational problems and with elliptic partial differential equations. The book not only reports the researches of the author but also the contributions of his contemporaries in the same and related fields. The book undoubtedly will become a standard reference for researchers in these areas. …The book is addressed mainly to mature mathematical analysts. However, any student of analysis will be greatly rewarded by a careful study of this book. 'M. R. Hestenes in Journal of Optimization Theory and Applications 'The work intertwines in masterly fashion results of classical analysis, topology, and the theory of manifolds and thus presents a comprehensive treatise of the theory of multiple integral variational problems. 'L. Schmetterer in Monatshefte für Mathematik' The book is very clearly exposed and contains the last modern theory in this domain. A comprehensive bibliography ends the book.'M. Coroi-Nedeleu in Revue Roumaine de Mathématiques Pures et Appliquées"

Udriște, C. and Tevy, I. (2023)

Variational calculus with engineering applications.

Hoboken, NJ: John Wiley & Sons.

 

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"A comprehensive overview of foundational variational methods for problems in engineering Variational calculus is a field in which small alterations in functions and functionals are used to find their relevant maxima and minima. It is a potent tool for addressing a range of dynamic problems with otherwise counter-intuitive solutions, particularly ones incorporating multiple confounding variables. Its value in engineering fields, where materials and geometric configurations can produce highly specific problems with unconventional or unintuitive solutions, is considerable. Variational Calculus with Engineering Applications provides a comprehensive survey of this toolkit and its engineering applications. Balancing theory and practice, it offers a thorough and accessible introduction to the field pioneered by Euler, Lagrange and Hamilton, offering tools that can be every bit as powerful as the better-known Newtonian mechanics. It is an indispensable resource for those looking for engineering-oriented overview of a subject whose capacity to provide engineering solutions is only increasing. Variational Calculus with Engineering Applications readers will also find: Discussion of subjects including variational principles, levitation, geometric dynamics, and more Examples and instructional problems in every chapter, along with MAPLE codes for performing the simulations described in each Engineering applications based on simple, curvilinear, and multiple integral functionals Variational Calculus with Engineering Applications is ideal for advanced students, researchers, and instructors in engineering and materials science."