Civil Engineering Association

Applied Calculus of Variations for Engineers

Author:Louis Komzsik
Hardcover: 175 pages
Publisher: CRC Press; 1 edition (October 27, 2008)
Language: English
ISBN-10: 1420086626
ISBN-13: 978-1420086621

Book Description

The subject of calculus of variations is to find optimal solutions to engineering problems where the optimum may be a certain quantity, a shape, or a function. Applied Calculus of Variations for Engineers addresses this very important mathematical area applicable to many engineering disciplines. Its unique, application-oriented approach sets it apart from the theoretical treatises of most texts. It is aimed at enhancing the engineer’s understanding of the topic as well as aiding in the application of the concepts in a variety of engineering disciplines.

The first part of the book presents the fundamental variational problem and its solution via the Euler–Lagrange equation. It also discusses variational problems subject to constraints, the inverse problem of variational calculus, and the direct solution techniques of variational problems, such as the Ritz, Galerkin, and Kantorovich methods. With an emphasis on applications, the second part details the geodesic concept of differential geometry and its extensions to higher order spaces. It covers the variational origin of natural splines and the variational formulation of B-splines under various constraints. This section also focuses on analytic and computational mechanics, explaining classical mechanical problems and Lagrange’s equations of motion.

About the Author
Steady State, Transients, and Design with MATLAB

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The thoery of calculus of variations is somewhat complicated, It can be
rarely used in the civil engineering design process. But for some civil engineer dedicated in the field of theoretical rearch such as finite element methods , it can be used sometimes. So I post this book with the hope that it can do some help for those few engineers.

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Applied Calculus of Variations for Engineers, Second Edition (2014)

The purpose of the calculus of variations is to find optimal solutions to engineering problems whose optimum may be a certain quantity, shape, or function. Applied Calculus of Variations for Engineers addresses this important mathematical area applicable to many engineering disciplines. Its unique, application-oriented approach sets it apart from the theoretical treatises of most texts, as it is aimed at enhancing the engineer’s understanding of the topic.

This Second Edition text:

- Contains new chapters discussing analytic solutions of variational problems and Lagrange-Hamilton equations of motion in depth
- Provides new sections detailing the boundary integral and finite element methods and their calculation techniques
- Includes enlightening new examples, such as the compression of a beam, the optimal cross section of beam under bending force, the solution of Laplace’s equation, and Poisson’s equation with various methods

Applied Calculus of Variations for Engineers, Second Edition extends the collection of techniques aiding the engineer in the application of the concepts of the calculus of variations.

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