Book description
This book is issued from a 30 years’ experience on the presentation of variational methods to successive generations of students and researchers in Engineering. It gives a comprehensive, pedagogical and engineeroriented presentation of the foundations of variational methods and of their use in numerical problems of Engineering. Particular applications to linear and nonlinear systems of equations, differential equations, optimization and control are presented. MATLAB programs illustrate the implementation and make the book suitable as a textbook and for selfstudy.
The evolution of knowledge, of the engineering studies and of the society in general has led to a change of focus from students and researchers. New generations of students and researchers do not have the same relations to mathematics as the previous ones. In the particular case of variational methods, the presentations used in the past are not adapted to the previous knowledge, the language and the centers of interest of the new generations. Since these methods remain a core knowledge – thus essential  in many fields (Physics, Engineering, Applied Mathematics, Economics, Image analysis …), a new presentation is necessary in order to address variational methods to the actual context.
Table of contents
 Cover
 Title
 Copyright
 Introduction

Chapter 1. Integrals
 1.1 Riemann integrals
 1.2 Lebesgue integrals
 1.3 Matlab® classes for a Riemann integral by trapezoidal integration
 1.4 Matlab® classes for Lebesgue’s integral
 1.5 Matlab® classes for evaluation of the integrals when/is defined by a subprogram
 1.6 Matlab® classes for partitions including the evaluation of the integrals
 Chapter 2. Variational Methods for Algebraic Equations
 Chapter 3. Hilbert Spaces for Engineers

Chapter 4. Functional Spaces for Engineers
 4.1 The L2 (Ω) space (Ω) space
 4.2 Weak derivatives
 4.3 Sobolev spaces
 4.4 Variational equations involving elements of a functional space
 4.5 Reducing multiple indexes to a single one
 4.6 Existence and uniqueness of the solution of a variational equation
 4.7 Linear variational equations in separable spaces
 4.8 Parametric variational equations
 4.9 A Matlab® class for variational equations
 4.10 Exercises
 Chapter 5. Variational Methods for Differential Equations
 Chapter 6. Dirac’s Delta

Chapter 7. Functionals and Calculus of Variations
 7.1 Differentials
 7.2 Gâteaux derivatives of functionals
 7.3 Convex functionals
 7.4 Standard methods for the determination of Gâteaux derivatives
 7.5 Numerical evaluation and use of Gâteaux differentials
 7.6 Minimum of the energy
 7.7 Lagrange’s multipliers
 7.8 Primal and dual problems
 7.9 Matlab® determination of minimum energy solutions
 7.10 Firstorder control problems
 7.11 Secondorder control problems
 7.12 A variational approach for multiobjective optimization
 7.13 Matlab® implementation of the variational approach for biobjective optimization
 7.14 Exercises
 Bibliography
 Index
Product information
 Title: Variational Methods for Engineers with Matlab
 Author(s):
 Release date: October 2015
 Publisher(s): WileyISTE
 ISBN: 9781848219144
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