Calculus of Variations (Paperback)
暫譯: 變分法 (平裝本)
I. M. Gelfand, S. V. Fomin
- 出版商: Dover Publications
- 出版日期: 2000-10-16
- 售價: $820
- 貴賓價: 9.5 折 $779
- 語言: 英文
- 頁數: 256
- 裝訂: Paperback
- ISBN: 0486414485
- ISBN-13: 9780486414485
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相關分類:
微積分 Calculus
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商品描述
Based on a series of lectures given by I. M. Gelfand at Moscow State University, this book actually goes considerably beyond the material presented in the lectures. The aim is to give a treatment of the elements of the calculus of variations in a form both easily understandable and sufficiently modern. Considerable attention is devoted to physical applications of variational methods, e.g., canonical equations, variational principles of mechanics, and conservation laws.
The reader who merely wishes to become familiar with the most basic concepts and methods of the calculus of variations need only study the first chapter. Students wishing a more extensive treatment, however, will find the first six chapters comprise a complete university-level course in the subject, including the theory of fields and sufficient conditions for weak and strong extrema. Chapter 7 considers the application of variational methods to the study of systems with infinite degrees of freedom, and Chapter 8 deals with direct methods in the calculus of variations. The problems following each chapter were made specially for this English-language edition, and many of them comment further on corresponding parts of the text. Two appendices and suggestions for supplementary reading round out the text.
Substantially revised and corrected by the translator, this inexpensive new edition will be welcomed by advanced undergraduate and graduate students of mathematics and physics.
商品描述(中文翻譯)
根據 I. M. Gelfand 在莫斯科國立大學所做的一系列講座,本書的內容實際上超出了講座中所呈現的材料。其目的是以易於理解且足夠現代的形式,對變分法的基本元素進行處理。書中相當重視變分方法的物理應用,例如,正則方程、力學的變分原則以及守恆定律。
希望僅僅熟悉變分法最基本概念和方法的讀者,只需學習第一章。然而,對於希望深入了解的學生來說,前六章構成了一門完整的大學級課程,涵蓋了場的理論以及弱極值和強極值的充分條件。第七章考慮了變分方法在無限自由度系統研究中的應用,而第八章則處理變分法中的直接方法。每章後面的習題是專為這本英文版而設計的,許多習題進一步評論了文本中相應的部分。兩個附錄和補充閱讀建議為文本增添了內容。
這本經過翻譯者大幅修訂和校正的平價新版本,將受到數學和物理學高年級本科生及研究生的歡迎。