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商品描述
A stimulating introductory text, this volume examines many important applications of functional analysis to mechanics, fluid mechanics, diffusive growth, and approximation. Detailed enough to impart a thorough understanding, the text is also sufficiently straightforward for those unfamiliar with abstract analysis. Its four-part treatment begins with distribution theory and discussions of Green's functions. Essentially independent of the preceding material, the second and third parts deal with Banach spaces, Hilbert space, spectral theory, and variational techniques. The final part outlines the ideas behind Frechet calculus, stability and bifurcation theory, and Sobolev spaces. 25 Figures. 9 Appendices. Supplementary Problems. Indexes.
商品描述(中文翻譯)
這本引人入勝的入門書籍探討了函數分析在力學、流體力學、擴散增長和近似等許多重要應用。內容詳細,能夠 impart thorough understanding,同時對於不熟悉抽象分析的讀者來說也足夠簡單易懂。全書分為四個部分,首先介紹分佈理論和格林函數的討論。第二和第三部分基本上獨立於前面的內容,主要涉及巴拿赫空間(Banach spaces)、希爾伯特空間(Hilbert space)、譜理論(spectral theory)和變分技術(variational techniques)。最後一部分概述了弗雷歇微積分(Frechet calculus)、穩定性和分岔理論(bifurcation theory)以及索博列夫空間(Sobolev spaces)的基本概念。包含25幅圖、9個附錄、補充問題和索引。