Variational methods form the basis of all the modern numerical methods in engineering, namely finite elements, finite volumes and spectral methods.
This book introduces an original approach to variational formulations which starts from their application to linear algebraic equations. From these simple and comprehensive situations, the methods are then extended to their usual applications.
This text is a comprehensive guide for engineers and contains the complete presentation of numerical aspects with Matlab® programs to illustrate the implementation, making it suitable as a textbook and for self-study.
The authors provide a comprehensive and pedagogical presentation of the foundations of variational methods and of their use in numerical problems of engineering. Applications specific to linear and nonlinear systems of equations, differential equations, optimization and control are presented.
The exploration of the relationship between variational formulations and probabilities presented in this book opens new perspectives and provides a glimpse of exciting prospects for the future.
2. Variational Methods for Algebraic Equations.
3. Hilbert Spaces for Engineers.
4. Functional Spaces for Engineers.
5. Variational Methods for Differential Equations.
6. Dirac’s Delta.
7. Functionals and Calculus of Variations.
Eduardo Souza de Cursi is Professor at the National Institute for Applied Sciences in Rouen, France, where he is also Dean of International Affairs and Director of the Laboratory for the Optimization and Reliability in Structural Mechanics.
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