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curvilinear coordinates. This treatment includes in particular a direct proof of the three-dimensional Korn inequality in curvilinear coordinates. The fourth and last chapter, which heavily relies on Chapter 2, begins by a detailed description of the nonlinear and linear equations proposed by W.T. Koiter for modeling thin elastic shells. These equations are “two-dimensional”, in the sense that they are expressed in terms of two curvilinear coordinates used for de?ning the middle surface of the shell. The existence, uniqueness, and regularity of solutions to the linear Koiter equations is then established, thanks this time to a fundamental “Korn inequality on a surface” and to an “in?nit- imal rigid displacement lemma on a surface”. This chapter also includes a brief introduction to other two-dimensional shell equations. Interestingly, notions that pertain to di?erential geometry per se,suchas covariant derivatives of tensor ?elds, are also introduced in Chapters 3 and 4, where they appear most naturally in the derivation of the basic boundary value problems of three-dimensional elasticity and shell theory. Occasionally, portions of the material covered here are adapted from - cerpts from my book “Mathematical Elasticity, Volume III: Theory of Shells”, published in 2000by North-Holland, Amsterdam; in this respect, I am indebted to Arjen Sevenster for his kind permission to rely on such excerpts. Oth- wise, the bulk of this work was substantially supported by two grants from the Research Grants Council of Hong Kong Special Administrative Region, China [Project No. 9040869, CityU 100803 and Project No. 9040966, CityU 100604].

Elasticity. --- Geometry, Differential. --- Differential geometry --- Elastic properties --- Young's modulus --- Mathematical physics --- Matter --- Statics --- Rheology --- Strains and stresses --- Strength of materials --- Properties --- Engineering mathematics. --- Mechanics. --- Differential equations, partial. --- Global differential geometry. --- Mathematical and Computational Engineering. --- Classical Mechanics. --- Partial Differential Equations. --- Differential Geometry. --- Geometry, Differential --- Partial differential equations --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics --- Applied mathematics. --- Partial differential equations. --- Differential geometry.

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Differential equations, Elliptic --- Numerical solutions --- Boundary value problems --- Finite element method --- Elliptische Differentialgleichung --- Randwertproblem --- Numerisches Verfahren --- Finite-Elemente-Methode --- -Boundary value problems --- -517.9 --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear --- Differential equations, Partial --- -Data processing --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Finite element method. --- Numerical solutions. --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 517.9 --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Acqui 2006

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The objective of Volume III is to lay down the proper mathematical foundations of the two-dimensional theory of shells. To this end, it provides, without any recourse to any a priori assumptions of a geometrical or mechanical nature, a mathematical justification of two-dimensional nonlinear and linear shell theories, by means of asymptotic methods, with the thickness as the ""small"" parameter.

Elasticity. --- Shells. --- Conchology --- Sea shells --- Seashell collecting --- Seashells --- Shell collecting --- Body covering (Anatomy) --- Mollusks --- Conchologists --- Elastic properties --- Young's modulus --- Mathematical physics --- Matter --- Statics --- Rheology --- Strains and stresses --- Strength of materials --- Properties

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The purpose of this book is to give a thorough introduction to the most commonly used methods of numerical linear algebra and optimisation. The prerequisites are some familiarity with the basic properties of matrices, finite-dimensional vector spaces, advanced calculus, and some elementary notations from functional analysis. The book is in two parts. The first deals with numerical linear algebra (review of matrix theory, direct and iterative methods for solving linear systems, calculation of eigenvalues and eigenvectors) and the second, optimisation (general algorithms, linear and nonlinear programming). The author has based the book on courses taught for advanced undergraduate and beginning graduate students and the result is a well-organised and lucid exposition. Summaries of basic mathematics are provided, proofs of theorems are complete yet kept as simple as possible, and applications from physics and mechanics are discussed. Professor Ciarlet has also helpfully provided over 40 line diagrams, a great many applications, and a useful guide to further reading. This excellent textbook, which is translated and revised from the very successful French edition, will be of great value to students of numerical analysis, applied mathematics and engineering.

Algebras, Linear --- Mathematical Optimization --- Mathematics

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Differential geometry. Global analysis --- Partial differential equations --- Classical mechanics. Field theory --- Engineering sciences. Technology --- differentiaalvergelijkingen --- analyse (wiskunde) --- differentiaal geometrie --- ingenieurswetenschappen --- mechanica