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This textbook offers a concise and thorough introduction to the topic of applied functional analysis. Targeted to graduate students of mathematics, it presents standard topics in a self-contained and accessible manner. Featuring approximately 300 problems sets to aid in understanding the content, this text serves as an ideal resource for independent study or as a textbook for classroom use. With its comprehensive coverage and reader-friendly approach, it is equally beneficial for both students and teachers seeking a detailed and in-depth understanding of the subject matter.
List of contents
Chapter 1. Operator Theory.- Chapter 2. Distribution Theory.- Chapter 3. Theory of Sobolev Spaces.- Chapter 4. Elliptic Theory.- Chapter 5. Calculus of Variations.
About the author
Ammar Khanfer earned his Ph.D. from Wichita State University, USA. His area of interest is analysis and partial differential equations (PDEs), focusing on the interface and links between elliptic PDEs and hypergeometry. He has notably contributed to the field by providing prototypes studying the behavior of generalized solutions of elliptic PDEs in higher dimensions in connection to the behavior of hypersurfaces near nonsmooth boundaries. He also works on the qualitative theory of differential equations, and in the area of inverse problems of mathematical physics. He has published articles of high quality in reputable journals.
Ammar taught at several universities in the USA: Western Michigan University, Wichita State University, and Southwestern College in Winfield. He was a member of the Academy of Inquiry Based Learning (AIBL) in the USA. During the period 2008-2014, he participated in AIBL workshops and conferences on effective teaching methodologies and strategies of creative thinking, which made an impact on his engaging and motivational writing style. He then moved to Saudi Arabia to teach at Imam Mohammad Ibn Saud Islamic University, where he taught and supervised undergraduate and graduate students of mathematics. Furthermore, he was appointed as coordinator of the PhD program establishment committee in the department of mathematics. In 2020, he moved to Prince Sultan University in Riyadh, and has been teaching there since then.
