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.
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.
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.
"There is definitely a need for engineers and scientists alike to master a plethora of tools and techniques in their careers. The calculus of variations has long been viewed as esoteric and theoretical, hence explaining its absence from most universities' engineering curricula. But mentalities need to be changed as products developed today are becoming more and more sophisticated. Hence there is a need for more books in this field that are targeted to the engineering profession, and I expect that this second edition of Dr. Komzsik's book will gain widespread popularity. ... All scientific and non-scientific fields (such as financial engineering) can benefit from the concept of calculus of variations. This book, with its rather high level of math, will appeal most to those in engineering and the natural sciences."
-Dr. Yogeshwarsing Calleecharan, Department of Engineering Sciences and Mathematics, Lulea University of Technology, Sweden
"The author has explained a very difficult subject in a manner which can be understood, even by those with limited backgrounds. ... The book's subject is one of the basic building blocks for deeper understanding of the finite element method. ... This topic has been written about by many mathematicians. However, a complete discussion of this topic, clearly explained by a practical engineer, is definitely a plus for both the engineering and mathematical communities."
-Prof. Duc T. Nguyen Old Dominion University, Norfolk, Virginia, USA