Pub. Date:
Taylor & Francis
Applied Calculus of Variations for Engineers

Applied Calculus of Variations for Engineers

by Louis Komzsik


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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.

Product Details

ISBN-13: 9781420086621
Publisher: Taylor & Francis
Publication date: 10/27/2008
Pages: 175
Product dimensions: 6.40(w) x 9.30(h) x 0.70(d)

About the Author

Dr. Louis Komzsik is a graduate of the Technical University of Budapest, Hungary and the Eötvös Loránd University, Budapest, Hungary. He has been working in the industry for more than 40 years, and is currently the chief numerical analyst in the Office of Architecture and Technology at Siemens PLM Software, Cypress, California, USA. Dr. Komzsik is the author of the NASTRAN Numerical Methods Handbook, first published by MSC in 1987. His book, The Lanczos Method, published by SIAM, has also been translated into Japanese, Korean, and Hungarian. His book, Computational Techniques of Finite Element Analysis, published by CRC Press, is in its second print, and his Approximation Techniques for Engineers was published by Taylor and Francis in 2006. He is also the coauthor of the book Computational Techniques of Rotor Dynamics with the Finite Element Method, published by Taylor and Francis in 2012.

Table of Contents

The Foundations of Calculus of Variations. Constrained Variational Problems. Multivariate Functionals. Higher Order Derivatives. The Inverse Problem of Calculus of Variations. Analytic Solutions of Variational Problems. Numerical Methods of Calculus of Variations. Differential Geometry. Computational Geometry. Variational Equations of Motion. Analytic Mechanics. Computational Mechanics.

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