Mathematical analysis : foundations and advanced techniques for functions of several variables
著者
書誌事項
Mathematical analysis : foundations and advanced techniques for functions of several variables
Birkhäuser , Springer, c2012
大学図書館所蔵 件 / 全7件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes index (p. 399-405)
Bibliographical notes : p. 397-398
内容説明・目次
内容説明
Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volume. The presentation is largely focused on the foundations of measure and integration theory.
The book begins with a discussion of the geometry of Hilbert spaces, convex functions and domains, and differential forms, particularly k-forms. The exposition continues with an introduction to the calculus of variations with applications to geometric optics and mechanics. The authors conclude with the study of measure and integration theory - Borel, Radon, and Hausdorff measures and the derivation of measures. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis.
This work may be used as a supplementary text in the classroom or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. One of the key strengths of this presentation, along with the other four books on analysis published by the authors, is the motivation for understanding the subject through examples, observations, exercises, and illustrations.
目次
Preface.- Spaces of Summable Functions and Partial Differential Equations.- Convex Sets and Convex Functions.- The Formalism of the Calculus of Variations.- Differential Forms.- Measures and Integrations.- Hausdorff and Radon Measures.- Mathematicians and Other Scientists.- Bibliographical Notes.- Index.
「Nielsen BookData」 より