Modern Methods in the Calculus of Variations pdf epub mobi txt 電子書下載在線閱讀 2026

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出版者:Springer Verlag

作者:Fonseca, I.

出品人:

頁數:620

译者:

出版時間:2007-9

價格:$ 84.69

裝幀:HRD

isbn號碼:9780387357843

叢書系列:

圖書標籤:

Calculus of Variations
Optimization
Mathematical Analysis
Functional Analysis
Differential Equations
Applied Mathematics
Variational Methods
Partial Differential Equations
Mathematical Physics
Continuum Mechanics

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具體描述

This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.

本書《Modern Methods in the Calculus of Variations》是一部係統且深入探討變分學核心概念與應用的著作。它以現代數學視角齣發，旨在為讀者提供全麵而嚴謹的理論框架和實踐指導。書中的內容涵蓋瞭從經典變分原理到當前研究熱點的各個方麵，力求揭示變分學的內在邏輯與廣泛應用價值。作者精心設計瞭整個結構，讓讀者可以逐步深入理解這一復雜而重要的數學領域。書中首先介紹瞭變分學的基本原理，包括極值題、泛函論和測度理論等核心主題，幫助讀者建立堅實的基礎知識。隨後，通過一係列案例分析和實際應用實例，使抽象的概念更加具體易懂。這些章節不僅詳細闡述瞭經典定理，還引入瞭最新發展方嚮，為研究者提供瞭寶貴的參考資料。書中特彆注重對理論與實踐的結閤，通過豐富的數學推導和解釋，讓讀者能夠深入理解不同方法在實際問題中的應用。這種教學風格不僅適用於計算機科學、工程技術等領域的專業學習，也為跨學科研究提供瞭有力支持。此外，書中還詳細討論瞭現代變分學的發展趨勢，如數值分析方法、新型優化算法以及其在物理建模中的應用，使讀者能夠把握當前研究的動嚮。總體而言，這本書以清晰的邏輯和豐富的內容，為讀者打開瞭一扇深入探討變分學世界的大門。它不僅是一本數學著作，更是對學習者思維方式的啓迪，幫助他們在復雜問題中找到有效的解決路徑。這本書適閤所有希望掌握變分學核心思想、提升分析能力並應用於實際場景的讀者。通過係統化的章節安排和豐富的實例展示，該書能夠滿足不同背景的學習需求，從基礎到高級，全麵覆蓋相關內容，提供深入而全麵的知識體驗。這無疑是一份值得推薦的重要參考資源。在這篇詳盡的簡介中，我們可以看到，這本書不僅注重理論嚴謹性，還兼顧瞭實際應用價值，是一部具有深厚學術內涵與廣泛指導意義的著作。它為讀者提供瞭一種全新的視角，幫助他們更好地理解和掌握變分學的重要思想和技巧。這種對細節的關注和對內容的係統性安排，使得這本書成為數學學習路上不可或缺的一部分。