Bøger af Philippe G. Ciarlet

Contains three self-contained volumes that together provide the only modern treatise on elasticity. They introduce contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells. Each volume contains proofs, detailed surveys of all mathematical prerequisites, and problems for teaching and self-study.

The objective of Theory of Shells is to show how asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear shell theories: membrane, generalized membrane, and flexural. The book contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study.

Provides a rigorous mathematical justification of the classical two-dimensional linear plate and shallow shell theories. The volume contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study.

Covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. The volume contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study.

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, Fourier transform, Hilbert transform, and Calderon-Zygmund singular integrals.

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 is the only book available that analyses in depth the mathematical foundations of the finite element method. It is a valuable reference and introduction to current research on the numerical analysis of the finite element method, as well as a working textbook for graduate courses in numerical analysis.