E-raamat: Variational Calculus with Engineering Applications

"The Variational Calculus with Engineering Applications was and is being taught to 4th year engineering students, in the Faculty of Applied Sciences, Mathematics - Informatics Department, from the University Politehnica of Bucharest, by Prof. Emeritus Dr. Constantin Udriste. Certain topics are taught at other faculties of our university, especially at master's or doctoral courses, being present in the papers that can be published in journals now categorized as "ISI". The Chapters were structured according to the importance, accessibility and impact of the theoretical notions able to outline a future specialist based on mathematical optimization tools. The probing and intermediate variants lasted for a number of sixteen years, leading to the selection of the most important manageable notions and reaching maturity through this variant that we decided to publish at Wiley. Now the topics of the book includes seven Chapters: Extrema of Dierentiable Functionals; Variational Principles; Optimal Models Based on Energies; Variational Integrators; Miscellaneous Topics; Extremals with Nonholonomic Constraints; Problems: Free and Constrained Extremals. To cover modern problem-solving methods, each Chapter includes Maple application topics."--

VARIATIONAL CALCULUS WITH ENGINEERING APPLICATIONS

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.