Variational methods for engineers with Matlab
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 engineer-oriented presentation of the foundations of variational methods and of their use in nume...
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
London, England ; Hoboken, New Jersey :
iSTE
2015.
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| Edición: | 1st edition |
| Colección: | Numerical methods in engineering series.
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| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009629854906719 |
Tabla de Contenidos:
- ""Table of Contents""; ""Title""; ""Copyright""; ""Introduction""; ""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""; ""2: Variational Methods for Algebraic Equations""; ""2.1 Linear systems""; ""2.2 Algebraic equations depending upon a parameter""; ""2.3 Exercises""
- ""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""; ""5: Variational Methods for Differential Equations""; ""5.1 A simple situation: the oscillator with one degree of freedom""; ""5.2 Connection between differential equations and variational equations""; ""5.3 Variational approximation of differential equations""
- ""5.4 Evolution partial differential equations""""5.5 Exercises""; ""6: Dirac's Delta""; ""6.1 A simple example""; ""6.2 Functional definition of Dirac's delta""; ""6.3 Approximations of Dirac's delta""; ""6.4 Smoothed particle approximations of Dirac's delta""; ""6.5 Derivation using Dirac's delta approximations""; ""6.6 A Matlab® class for smoothed particle approximations""; ""6.7 Green's functions""; ""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 First-order control problems""; ""7.11 Second-order 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""
