LEADER 05270nam 2200589 450 001 9910131500303321 005 20200520144314.0 010 $a1-119-23015-2 010 $a1-119-23012-8 010 $a1-119-23014-4 035 $a(CKB)3710000000486260 035 $a(EBL)4043125 035 $a(Au-PeEL)EBL4043125 035 $a(CaPaEBR)ebr11115265 035 $a(CaONFJC)MIL839950 035 $a(OCoLC)926070987 035 $a(CaSebORM)9781848219144 035 $a(MiAaPQ)EBC4043125 035 $a(PPN)194065391 035 $a(EXLCZ)993710000000486260 100 $a20151109h20152015 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aVariational methods for engineers with Matlab /$fEduardo Souza de Cursi 205 $a1st edition 210 1$aLondon, England ;$aHoboken, New Jersey :$ciSTE :$cWiley,$d2015. 210 4$d©2015 215 $a1 online resource (335 p.) 225 1 $aNumerical Methods in Engineering Series 300 $aDescription based upon print version of record. 311 $a1-84821-914-8 320 $aIncludes bibliographical references and index. 327 $a""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"" 327 $a""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"" 327 $a""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 Ga?teaux derivatives of functionals""; ""7.3 Convex functionals"" 327 $a""7.4 Standard methods for the determination of Ga?teaux derivatives""""7.5 Numerical evaluation and use of Ga?teaux 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"" 330 $aThis book is issued from a 30 years? experience on the presentation of variational methods to successive generations of students and researchers in Engineering. It gives a comprehensive, pedagogical and engineer-oriented presentation of the foundations of variational methods and of their use in numerical problems of Engineering. Particular applications to linear and nonlinear systems of equations, differential equations, optimization and control are presented. MATLAB programs illustrate the implementation and make the book suitable as a textbook and for self-study. The evolution of knowledge, of the engineering studies and of the society in general has led to a change of focus from students and researchers. New generations of students and researchers do not have the same relations to mathematics as the previous ones. In the particular case of variational methods, the presentations used in the past are not adapted to the previous knowledge, the language and the centers of interest of the new generations. Since these methods remain a core knowledge ? thus essential - in many fields (Physics, Engineering, Applied Mathematics, Economics, Image analysis ?), a new presentation is necessary in order to address variational methods to the actual context. 410 0$aNumerical methods in engineering series. 606 $aVariational inequalities (Mathematics) 615 0$aVariational inequalities (Mathematics) 676 $a515.64 700 $aCursi$b Eduardo Souza de$0908276 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910131500303321 996 $aVariational methods for engineers with Matlab$92031430 997 $aUNINA