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This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. The main purpose is on the one hand to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences; on the other hand to give them a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first one has a rather elementary character with the goal of developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. Ideas and connections with concrete aspects are emphasized whenever possible, in order to provide intuition and feeling for the subject. For this part, a knowledge of advanced calculus and ordinary differential equations is required. Also, the repeated use of the method of separation of variables assumes some basic results from the theory of Fourier series, which are summarized in an appendix. The main topic of the second part is the development of Hilbert space methods for the variational formulation and analysis of linear boundary and initial-boundary value problemsemph{. }% Given the abstract nature of these chapters, an effort has been made to provide intuition and motivation for the various concepts and results. The understanding of these topics requires some basic knowledge of Lebesgue measure and integration, summarized in another appendix. At the end of each chapter, a number of exercises at different level of complexity is included. The most demanding problems are supplied with answers or hints. The exposition if flexible enough to allow substantial changes without compromising the comprehension and to facilitate a selection of topics for a one or two semester course.

differentiaalvergelijkingen --- Partial differential equations --- Differential equations, Partial --- Equations aux dérivées partielles --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B

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The maximum principle induces an order structure for partial differential equations, and has become an important tool in nonlinear analysis. This book is the first of two volumes to systematically introduce the applications of order structure in certain nonlinear partial differential equation problems. The maximum principle is revisited through the use of the Krein-Rutman theorem and the principal eigenvalues. Its various versions, such as the moving plane and sliding plane methods, are applied to a variety of important problems of current interest. The upper and lower solution method, espec

Differential equations, Nonlinear --- Differential equations, Partial --- Numerical analysis --- Numerical solutions. --- Equations aux dérivées partielles --- Equations différentielles non linéaires --- Numerical solutions --- Solutions numériques

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Nonlinear Partial Differential Equations in Engineering: v. 1

Differential equations, Nonlinear. --- Differential equations, Partial. --- Differential equations, Partial --- Differential equations, Nonlinear --- Partial differential equations --- Nonlinear differential equations --- Nonlinear theories --- Equations aux dérivées partielles --- Equations différentielles non linéaires --- EPUB-LIV-FT ELSEVIER-B

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Partial differential equations --- Differential equations, Partial --- Equations aux dérivées partielles --- Équations différentielles partielles --- Théorie --- --6076 --- 517.95 --- #TCPW W7.0 --- Differential equations, Partial. --- 517.95 Partial differential equations --- Equations aux dérivées partielles --- Équation différentielle partielle --- --Théorie --- --Differential equations, Partial --- Équations aux dérivées partielles --- Équations aux dérivées partielles --- Equations aux derivees partielles elliptiques --- Equations aux derivees partielles hyperboliques

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Differential equations, Partial --- Hilbert space --- Equations aux dérivées partielles --- Espace de Hilbert --- 517.95 --- Banach spaces --- Hyperspace --- Inner product spaces --- Partial differential equations --- Differential equations, Partial. --- Hilbert space. --- Solution --- Hilbert space methods --- Hilbert space methods. --- 517.95 Partial differential equations --- Equations aux dérivées partielles