05270nam 2200589 450 991081788390332120200520144314.01-119-23015-21-119-23012-81-119-23014-4(CKB)3710000000486260(EBL)4043125(Au-PeEL)EBL4043125(CaPaEBR)ebr11115265(CaONFJC)MIL839950(OCoLC)926070987(CaSebORM)9781848219144(MiAaPQ)EBC4043125(PPN)194065391(EXLCZ)99371000000048626020151109h20152015 uy 0engur|n|---|||||rdacontentrdamediardacarrierVariational methods for engineers with Matlab /Eduardo Souza de Cursi1st editionLondon, England ;Hoboken, New Jersey :iSTE :Wiley,2015.©20151 online resource (335 p.)Numerical Methods in Engineering SeriesDescription based upon print version of record.1-84821-914-8 Includes bibliographical references and index.""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""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 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 self-study. 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.Numerical methods in engineering series.Variational inequalities (Mathematics)Variational inequalities (Mathematics)515.64Cursi Eduardo Souza de908276MiAaPQMiAaPQMiAaPQBOOK9910817883903321Variational methods for engineers with Matlab2031430UNINA