Philippe G. Ciarlet's Books

Theory of Shells

By: Philippe G. Ciarlet

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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.

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662

Publisher

Elsevier

Published Date

ISBN 10

0080511236

ISBN 13

9780080511238

Differential Geometry

Theory and Applications

By: Philippe G. Ciarlet

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Differential Geometry

Theory and Applications

By: Philippe G. Ciarlet

This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a self-contained and accessible manner. Although the field is often considered a ?classical? one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role.The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and mesh generation in finite element methods.This volume will be very useful to graduate students and researchers in pure and applied mathematics.

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302

Publisher

World Scientific

Published Date

ISBN 10

9812771468

ISBN 13

9789812771469

The Finite Element Method for Elliptic Problems

By: Philippe G. Ciarlet

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The Finite Element Method for Elliptic Problems

By: Philippe G. Ciarlet

This is the only book available that fully analyzes the mathematical foundations of the finite element method. Not only is it valuable reference and introduction to current research, it is also a working textbook for graduate courses in numerical analysis, including useful figures and exercises of varying difficulty.

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Page Count

552

Publisher

SIAM

Published Date

ISBN 10

0898715148

ISBN 13

9780898715149

Locally Convex Spaces and Harmonic Analysis: An Introduction

By: Philippe G. Ciarlet

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Locally Convex Spaces and Harmonic Analysis: An Introduction

By: Philippe G. Ciarlet

This self-contained textbook covers the fundamentals of two basic topics of linear functional analysis: locally convex spaces and harmonic analysis. Readers will find detailed introductions to topological vector spaces, distribution theory, weak topologies, the Fourier transform, the Hilbert transform, and Calderón–Zygmund singular integrals. An ideal introduction to more advanced texts, the book complements Ciarlet’s Linear and Nonlinear Functional Analysis with Applications (SIAM), in which these two topics were not treated. Pedagogical features such as detailed proofs and 93 problems make the book ideal for a one-semester first-year graduate course or for self-study. The book is intended for advanced undergraduates and first-year graduate students and researchers. It is appropriate for courses on functional analysis, distribution theory, Fourier transform, and harmonic analysis.

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Page Count

203

Publisher

SIAM

Published Date

ISBN 10

1611976650

ISBN 13

9781611976656

Linear and Nonlinear Functional Analysis with Applications

By: Philippe G. Ciarlet

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Linear and Nonlinear Functional Analysis with Applications

By: Philippe G. Ciarlet

This single-volume textbook covers the fundamentals of linear and nonlinear functional analysis, illustrating most of the basic theorems with numerous applications to linear and nonlinear partial differential equations and to selected topics from numerical analysis and optimization theory. This book has pedagogical appeal because it features self-contained and complete proofs of most of the theorems, some of which are not always easy to locate in the literature or are difficult to reconstitute. It also offers 401 problems and 52 figures, plus historical notes and many original references that provide an idea of the genesis of the important results, and it covers most of the core topics from functional analysis.

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847

Publisher

SIAM

Published Date

ISBN 10

1611972590

ISBN 13

9781611972597

An Introduction to Differential Geometry with Applications to Elasticity

By: Philippe G. Ciarlet

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An Introduction to Differential Geometry with Applications to Elasticity

By: Philippe G. Ciarlet

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].

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Page Count

212

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402042485

ISBN 13

9781402042485

Mathematical Elasticity

Theory of Plates

By: Philippe G. Ciarlet

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Mathematical Elasticity

Theory of Plates

By: Philippe G. Ciarlet

In this second book of a three-volume set, asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear plate and shallow shell theories. Theory of Plates also illustrates how asymptotic methods allow for justification of the Kirchhoff–Love theory of nonlinear elastic plates and presents a detailed mathematical analysis of the von Kármán equations. An extended preface and extensive bibliography have been added to highlight the progress that has been made since the volume’s original publication. While each one of the three volumes is self-contained, together the Mathematical Elasticity set provides the only modern treatise on elasticity; introduces contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells; and contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.

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Page Count

575

Publisher

SIAM

Published Date

ISBN 10

1611976804

ISBN 13

9781611976809

Introduction to Numerical Linear Algebra and Optimisation

By: Philippe G. Ciarlet,Bernadette Miara,Jean-Marie Thomas

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Introduction to Numerical Linear Algebra and Optimisation

By: Philippe G. Ciarlet,Bernadette Miara,Jean-Marie Thomas

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.

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Page Count

456

Publisher

Cambridge University Press

Published Date

ISBN 10

0521339847

ISBN 13

9780521339841

Three-Dimensional Elasticity

By: Philippe G. Ciarlet

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Three-Dimensional Elasticity

By: Philippe G. Ciarlet

This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible.

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Page Count

500

Publisher

Elsevier

Published Date

ISBN 10

044481776X

ISBN 13

9780444817761

Linear and Nonlinear Functional Analysis with Applications

By: Philippe G. Ciarlet

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Linear and Nonlinear Functional Analysis with Applications

By: Philippe G. Ciarlet

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Page Count

847

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SIAM

Published Date

ISBN 10

1611972582

ISBN 13

9781611972580

Book's by Philippe G. Ciarlet

Theory of Shells

Theory of Shells

Differential Geometry

Differential Geometry

The Finite Element Method for Elliptic Problems

The Finite Element Method for Elliptic Problems

Locally Convex Spaces and Harmonic Analysis: An Introduction

Locally Convex Spaces and Harmonic Analysis: An Introduction

Linear and Nonlinear Functional Analysis with Applications

Linear and Nonlinear Functional Analysis with Applications

An Introduction to Differential Geometry with Applications to Elasticity

An Introduction to Differential Geometry with Applications to Elasticity

Mathematical Elasticity

Mathematical Elasticity

Introduction to Numerical Linear Algebra and Optimisation

Introduction to Numerical Linear Algebra and Optimisation

Three-Dimensional Elasticity

Three-Dimensional Elasticity

Linear and Nonlinear Functional Analysis with Applications

Linear and Nonlinear Functional Analysis with Applications

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