02473cam a22002895i 450000500170000000800410001702000180005804100080007608200170008410000180010124501110011925000120023026000370024230000170027944000390029650504600033552010720079565000240186765000280189165000240191965000250194365000360196865000530200465000470205765000550210470000240215920250104155205.0150424s2015    gw |||| o    |||| 0|eng    a9783031218521  aeng04a003.3bSalP41 aSalsa, Sandro10aPartial Differential Equations in Action :bFrom Modelling to Theory /cSandro Salsa and Gianmaria Verzini  a4th Ed.  aSwitzerland :bSpringer,cc2009.  axviii, 677p.  aLa Matematica per il 3+2vVol. 1470 a1 Introduction -- 2 Diffusion -- 3 The Laplace Equation -- 4 Scalar Conservation Laws and First Order Equations -- 5 Waves and vibrations -- 6 Elements of Functional Analysis -- 7 Distributions and Sobolev Spaces -- 8 Variational formulation of elliptic problems -- 9 Further Applications -- 10 Weak Formulation of Evolution Problems -- 11 Systems of Conservation Laws -- 12 A Fourier Series -- 13 B Measures and Integrals -- 14 C Identities and Formulas.  aThe book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems. 0aApplied Mathematics 0aEngineering Mathematics 0aMathematical Models 0aMathematical Physics 0aPartial Differential Equations.14aMathematical Modeling and Industrial Mathematics24aMathematical and Computational Engineering24aMathematical Applications in the Physical Sciences  aVerzini, Gianmaria