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商品描述
Introduction to Functional Analysis: Theory and Applications is a comprehensive and modern introduction to one of the most important foundations of contemporary mathematics. Originally published in Spanish and widely adopted throughout the Latin American academic community, this English edition presents a thoroughly revised and expanded translation of the acclaimed second edition.
Designed to serve both as a graduate-level textbook and a long-term reference work, the book develops the fundamental results of Functional Analysis while emphasizing their role in mathematics, physics, engineering, and computational science. Core topics include duality, linear operators, variational problems, compact operators, spectral theory, weak topologies, distribution theory, and Sobolev spaces, complemented by numerous applications to partial differential equations, numerical analysis, and finite element methods.
A distinguishing feature of the text is its unified and interconnected approach. Rather than treating subjects as isolated topics, the author carefully links concepts, proofs, and results across chapters, helping readers develop a deeper understanding of the discipline as a coherent whole. Banach and Hilbert space theory are intentionally woven together, enabling readers to appreciate both their common foundations and their essential differences. Likewise, important applied topics such as Babuska-Brezzi theory, distribution theory and Sobolev spaces are revisited throughout the book from multiple perspectives, reinforcing understanding and highlighting their broad relevance.
Drawing on decades of teaching and internationally recognized research, Gabriel N. Gatica combines rigorous mathematical exposition with practical applications, detailed proofs, and research-inspired exercises. The result is a distinctive and engaging text that supports advanced undergraduate and graduate study while providing researchers and practitioners with a valuable reference across a wide range of mathematical and engineering disciplines.
Ideal for courses in Functional Analysis, Applied Mathematics, Partial Differential Equations, Optimization, Numerical Analysis, Finite Element Methods, and Mathematical Methods in Physics and Engineering.
商品描述(中文翻譯)
Functional Analysis 入門：理論與應用
《Functional Analysis 入門：理論與應用》是一本全面且現代化的教材，介紹當代數學最重要的基礎之一。本書最初以西班牙文出版，並廣泛獲拉丁美洲學術界採用；本英文版則是廣受好評之第二版的完整修訂與擴充譯本。
本書可同時作為研究所程度的教科書與長期參考書，闡述 Functional Analysis 的基本成果，並強調其在數學、物理、工程與計算科學中的作用。核心主題包括對偶性、線性算子、變分問題、緊算子、譜理論、弱拓撲、分佈理論與 Sobolev 空間，並搭配大量偏微分方程、數值分析與有限元素法的應用。
本書的一項特色，是採取統一且彼此連貫的處理方式。作者不將各個主題視為互不相關的獨立單元，而是細心串聯不同章節中的概念、證明與結果，協助讀者更深入地理解這門學科的完整架構。Banach 空間與 Hilbert 空間理論也被有意地交織呈現，使讀者能同時掌握兩者共同的基礎與關鍵差異。同樣地，Babuška–Brezzi 理論、分佈理論與 Sobolev 空間等重要應用主題，也會在全書中從多種觀點反覆探討，以加深理解並突顯其廣泛的適用性。
Gabriel N. Gatica 憑藉數十年的教學經驗與國際公認的研究成果，將嚴謹的數學論述、實務應用、詳細證明，以及受研究啟發的習題融為一體。最終成果是一部獨具特色且引人入勝的著作，既適合高年級大學生與研究生進階學習，也能為數學與工程各領域的研究人員及實務工作者提供珍貴的參考資料。
適合 Functional Analysis、應用數學、偏微分方程、最佳化、數值分析、有限元素法，以及物理與工程中的數學方法等課程使用。
作者簡介
Gabriel N. Gatica is Full Professor in the Department of Mathematical Engineering and Senior Researcher at the Center for Research in Mathematical Engineering (CI²MA), University of Concepción, Chile. He is also an External Associate Researcher at the Center for Mathematical Modeling (CMM), University of Chile.
Professor Gatica is the author of more than 230 peer-reviewed research publications and six books. His research has made significant contributions to the development and analysis of innovative mixed finite element methods for a wide range of linear and nonlinear problems in continuum mechanics and electromagnetism. Over the past 25 years, he has published approximately 200 papers in this area, advancing both computational methods and their mathematical foundations. His work has also led to the establishment of new theoretical results whose impact extends well beyond his own research, influencing the broader fields of numerical analysis, partial differential equations, and applied mathematics.
Gabriel N. Gatica is recognized at both the national and international levels, as one of the main promoter of the development of Applied Mathematics, specially of Numerical Analysis of Partial Differential Equations, during the last 25 years in Chile, and particularly in Universidad de Concepción.
作者簡介(中文翻譯)
Gabriel N. Gatica 是智利康塞普西翁大學（University of Concepción）數學工程系的正教授，也是數學工程研究中心（Center for Research in Mathematical Engineering, CI²MA）的資深研究員。此外，他還是智利大學（University of Chile）數學建模中心（Center for Mathematical Modeling, CMM）的外部副研究員。
Gatica 教授著有六本書，並發表超過 230 篇經同儕審查的研究論文。他的研究對創新混合有限元素法（mixed finite element methods）的發展與分析做出了重要貢獻，這些方法廣泛應用於連續介質力學與電磁學中的各類線性及非線性問題。在過去 25 年間，他約發表了 200 篇相關領域的論文，推進了計算方法及其數學基礎的發展。他的研究也促成了新理論結果的建立，其影響力遠超過他個人的研究範疇，並對數值分析、偏微分方程式與應用數學等更廣泛的領域產生影響。
Gabriel N. Gatica 在智利國內與國際上均享有盛譽。在過去 25 年間，他是智利，尤其是康塞普西翁大學應用數學發展（特別是偏微分方程式的數值分析）的主要推動者之一。
