There is a resurgence of applications for the calculus of variations. In addition to solid mechanics and dynamics, it is applied to numerical methods, numerical grid generation, modern physics, various optimization settings, and fluid dynamics. The contents of this book reflect the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation.
There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings, and fluid dynamics, for example. Many of these applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. The content of the text reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. Most readers will be pleased to note that the mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. Therefore, the majority of the text consists of applications of variational calculus for a variety of fields.
Arvustused
'The current book is an attractive fresh look at the subject by a professor of mechanical and aerospace engineering Most chapters have a modest number of exercises. There is a very nice bibliography.' Bill Satzer, MAA Reviews 'This well-written book contains a large amount of material will also be useful for scientists from application areas, in particular, those from engineering and physics.' Viceniu D. Rdulescu, Mathematical Reviews 'Overall, the text is clear and provides an excellent introduction to the calculus of variations for engineers and applied scientists looking for a concise exposition of the theory with numerous applications. Several historical notes appear throughout the text, which helps students understand the overall framework of variational calculus.' Joel Storch, IEEE Systems Control Magazine
Muu info
This book reflects the strong connection between calculus of variations and the applications for which variational methods form the foundation.
1. Preliminaries;
2. Calculus of variations;
3. Rayleigh-Ritz, Galerkin,
and finite-element methods;
4. Hamilton's principle;
5. Classical mechanics;
6. Stability of dynamical systems;
7. Optics and electromagnetics;
8. Modern
physics;
9. Fluid mechanics;
10. Optimization and control;
11. Image
processing and data analysis;
12. Numerical grid generation.
A graduate of Lehigh University and former National Research Council Postdoctoral Fellow at the National Institute of Standards and Technology, Kevin W. Cassel is Associate Professor of Mechanical and Aerospace Engineering at the Illinois Institute of Technology (IIT). He has been a visiting researcher at the University of Manchester and University College London, and is a visiting professor at the University of Palermo, Italy. Professor Cassel's research utilizes computational fluid dynamics in conjunction with advanced analytical methods to address problems in bio-fluids, unsteady aerodynamics, multiphase flow, and cryogenic fluid flow and heat transfer. Dr Cassel is an Associate Fellow of the American Institute of Aeronautics and Astronautics, and his honors include IIT's University Excellence in Teaching Award (2008) and Ralph L. Barnett Excellence in Teaching Award (2007, 2001), the 2002 Alfred Noble Prize, and the Army Research Office Young Investigator Award (19982001).
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