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 material on measures, integration and convex functions, the book develops all of the necessary mathematical tools, including basic results for one-dimensional Sobolev spaces, absolutely continuous functions, and functions of bounded variation.

One-dimensional Variational Problems: An Introduction (Oxford Lecture Series in Mathematics and Its Applications)

Science & Math

Giaquinta, Mariano

Hildebrandt, Stefan

Buttazzo, Giuseppe

Mathematics

Clarendon Press

Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105 (Annals of Mathematics Studies, 105)

The description for this book, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105, will be forthcoming.

Princeton University Press

The description for this book, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105, will be forthcoming.

These lectures are an introduction to the regularity theory of minimizers of variational integrals, in the calculus of variations and of solutions of nonlinear elliptic systems. Topics covered include the Hilbert-space approach to boundary value problems and energy estimates.

Introduction to Regularity Theory for Nonlinear Elliptic Systems (Lectures in Mathematics)

Birkhauser

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 overspecialization and over-emphasis on abstraction. Applications and connections with other fields have been neglected . . . But . . . understanding of mathematics cannot be transmitted by painless entertainment any more than education in music can be brought by the most brilliant journalism to those who never have lis tened intensively. Actual contact with the content of living mathematics is necessary. Nevertheless technicalities and detours should be avoided, and the presentation of mathematics should be just as free from emphasis on routine as from forbidding dogmatism which refuses to disclose motive or goal and which is an unfair obstacle to honest effort. (From the preface to the first edition of What is Mathematics? by Richard Courant and Herbert Robbins, 1941.

Mathematical Analysis: Functions of One Variable

Modica, Giuseppe

* Embraces a broad range of topics in analysis requiring only a sound knowledge of calculus and the functions of one variable. * Filled with beautiful illustrations, examples, exercises at the end of each chapter, and a comprehensive index.

Mathematical Analysis

Mathematical Analysis: Linear and Metric Structures and Continuity

Examines linear structures, the topology of metric spaces, and continuity in infinite dimensions, with detailed coverage at the graduate level Includes applications to geometry and differential equations, numerous beautiful illustrations, examples, exercises, historical notes, and comprehensive index May be used in graduate seminars and courses or as a reference text by mathematicians, physicists, and engineers

Examines linear structures, the topology of metric spaces, and continuity in infinite dimensions, with detailed coverage at the graduate level Includes applications to geometry and differential equations, numerous beautiful illustrations, examples, exercises, historical notes, and comprehensive index May be used in graduate seminars and courses or as a reference text by mathematicians, physicists, and engineers

Mathematical Analysis: An Introduction to Functions of Several Variables

This superb and 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 the differential calculus of several variables, including that of Banach spaces.

Reference

Foreign Language Study & Reference

This superb and 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 the differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, and systems and stability of ordinary differential equations. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. This text motivates the study of the analysis of several variables with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.

See the best price to sell, buy, or rent books by Giaquinta, Mariano. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Giaquinta, Mariano

See the best price to sell, buy, or rent books by Giaquinta, Mariano. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

One-dimensional Variational Problems: An Introduction (Oxford Lecture Series in Mathematics and Its Applications)

Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105 (Annals of Mathematics Studies, 105)

Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105 (Annals of Mathematics Studies, 105)

Introduction to Regularity Theory for Nonlinear Elliptic Systems (Lectures in Mathematics)

Mathematical Analysis: Functions of One Variable

Mathematical Analysis

Mathematical Analysis: Linear and Metric Structures and Continuity

Mathematical Analysis: Linear and Metric Structures and Continuity

Mathematical Analysis: An Introduction to Functions of Several Variables

Mathematical Analysis: An Introduction to Functions of Several Variables