One-dimensional variational problems are often neglected in favor of problems which use multiple integrals and partial differential equations, which are typically more difficult to handle. However, these problems and their associated ordinary differential equations do exhibit many of the same challenges and complexity of higher-dimensional problems, while being accessible to more students. This book for graduate students provides the first modern introduction to this subject. It emphasizes direct methods and provides an exceptionally clear view of the underlying theory. Except for standard...
One-dimensional variational problems are often neglected in favor of problems which use multiple integrals and partial differential equations, which a...
The description for this book, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105, will be forthcoming.
The description for this book, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105, will be forth...
For more than two thousand years some familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today the traditional place of mathematics in education is in grave danger. Unfortunately, professional representatives of mathematics share in the reponsibiIity. The teaching of mathematics has sometimes degen erated into empty drill in problem solving, which may develop formal ability but does not lead to real understanding or to greater intellectual indepen dence. Mathematical research has shown a tendency toward...
For more than two thousand years some familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every c...
This volume aims at introducing some basic ideas for studying approxima tion processes and, more generally, discrete processes. The study of discrete processes, which has grown together with the study of infinitesimal calcu lus, has become more and more relevant with the use of computers. The volume is suitably divided in two parts. In the first part we illustrate the numerical systems of reals, of integers as a subset of the reals, and of complex numbers. In this context we intro duce, in Chapter 2, the notion of sequence which invites also a rethinking of the notions of limit and...
This volume aims at introducing some basic ideas for studying approxima tion processes and, more generally, discrete processes. The study of discrete...
This volume aims at introducing some basic ideas for studying approxima tion processes and, more generally, discrete processes. The study of discrete processes, which has grown together with the study of infinitesimal calcu lus, has become more and more relevant with the use of computers. The volume is suitably divided in two parts. In the first part we illustrate the numerical systems of reals, of integers as a subset of the reals, and of complex numbers. In this context we intro duce, in Chapter 2, the notion of sequence which invites also a rethinking of the notions of limit and...
This volume aims at introducing some basic ideas for studying approxima tion processes and, more generally, discrete processes. The study of discrete...
One of the fundamental ideas of mathematical analysis is the notion of a function; we use it to describe and study relationships among variable quantities in a system and transformations of a system. We have already discussed real functions of one real variable and a few examples of functions of several variables but there are many more examples of functions that the real world, physics, natural and social sciences, and mathematics have to offer: (a) not only do we associate numbers and points to points, but we as- ciate numbers or vectors to vectors, (b) in the calculus of variations and in...
One of the fundamental ideas of mathematical analysis is the notion of a function; we use it to describe and study relationships among variable quanti...
A monograph that deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs, and in physics, as stable equilibrium configurations in nonlinear elasticity or for liquid crystals. It treats the topics in an elementary way, illustrating results with simple examples.
A monograph that deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs,...
This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables.
The wide range of topics covered include: differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, differential forms on curves, a general introduction to holomorphic functions, including singularities and residues, surfaces and level sets, and systems and stability of ordinary differential equations. An appendix highlights...
This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for function...
This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike. Volume 1 deals with the for mal apparatus of the variational calculus and with nonparametric field theory, whereas Volume 2 treats parametric variational problems as weIl as Hamilton Jacobi theory and the classical theory of partial differential equations of first order. In a subsequent treatise we shall describe developments arising from Hilbert's 19th and 20th problems, especially direct methods and regularity theory. Of the classical variational calculus...
This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike. Volume 1 deal...
Non-scalar variational problems appear in different fields. In geometry, for in- stance, we encounter the basic problems of harmonic maps between Riemannian manifolds and of minimal immersions; related questions appear in physics, for example in the classical theory of a-models. Non linear elasticity is another example in continuum mechanics, while Oseen-Frank theory of liquid crystals and Ginzburg-Landau theory of superconductivity require to treat variational problems in order to model quite complicated phenomena. Typically one is interested in finding energy minimizing representatives in...
Non-scalar variational problems appear in different fields. In geometry, for in- stance, we encounter the basic problems of harmonic maps between Riem...
