Variational Calculus with Engineering Applications

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.

《工程應用的變分計算》

《工程應用的變分計算》是一本全面介紹基礎變分方法在工程問題中應用的綜合性概述。變分計算是一個利用函數和泛函的微小變化來找到相關極大值和極小值的領域。它是解決一系列動態問題的強大工具，這些問題在其他情況下可能有反直覺的解，特別是那些涉及多個混淆變量的問題。在工程領域，材料和幾何配置可能產生具有非常特定問題和非傳統或非直覺解的情況，因此變分計算在這些領域的價值是相當大的。

《工程應用的變分計算》提供了對這個工具包及其工程應用的全面調查。在理論和實踐之間取得平衡，它提供了對由歐拉、拉格朗日和哈密爾頓開創的領域的深入且易於理解的介紹，提供的工具可以和較為著名的牛頓力學一樣強大。對於那些尋求工程導向的主題概述的人來說，這是一個不可或缺的資源，該主題的工程解決能力只會不斷增強。

《工程應用的變分計算》的讀者還將找到：
- 討論包括變分原理、懸浮、幾何動力學等主題
- 每章節都有例子和教學問題，以及用於執行每個模擬的MAPLE代碼
- 基於簡單、曲線和多重積分泛函的工程應用

《工程應用的變分計算》非常適合工程和材料科學的高級學生、研究人員和教師。