Название: Variational Calculus with Engineering Applications
Автор: Constantin Udriste, Ionel Tevy
Издательство: Wiley
Год: 2023
Страниц: 224
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

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 Application s 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

Now the topics of the book include seven chapters: Extrema of Differentiable 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. The scientific authority we have as professors in technical university has allowed us to impose our point of view on the subject and on the types of reasoning that deserve to be offered to readers of variational calculus texts. Everything has been structured for the benefit of functional optimization that describes significant physical or engineering phenomena. To unlock the students’ minds we preferred a simplified language, specific to applied mathematics, sending readers of pure mathematics to the bibliography. Long experience as mathematics teachers in technical universities has prepared us to fluently expose ideas undressed by excessive formalizations, with great impact on the students’ understanding of the natural phenomena encountered in engineering and economics as well as their dressing in mathematical clothing. In this sense, we preferred mathematical modeling as a scientific support for intelligent presentation of the real world and we avoided the hint of abstract notions specific to pure mathematics.

Variational Calculus with Engineering Applications is ideal for advanced students, researchers, and instructors in engineering and materials science.