INTRODUCTORY FUNCTIONAL ANALYSIS WITH ~ APPLICATIONS

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Functional analysis plays an increasing role in the applied sciences as well as in mathematics itself. Consequently, it becomes more and more desirable to introduce the student to the field at an early stage of study. This book is intended to familiarize the reader with the basic concepts, principles and methods of functional analysis and its applications. Since a textbook should be written for the student, I have sought to bring basic parts of the field and related practical problems within the comfortable grasp of senior undergraduate students or beginning graduate students of mathematics and physics. I hope that graduate engineering students may also profit from the presentation. Prerequisites. The book is elementary. A background in under-graduate mathematics, in particular, linear algebra and ordinary cal-culus, is sufficient as a prerequisite. Measure theory is neither assumed nor discussed. No knowledge in topology is required; the few consider-ations involving compactness are self-contained. Complex analysis is not needed, except in one of the later sections (Sec. 7.5), which is optional, so that it can easily be omitted. Further help is given in Appendix 1, which contains simple material for review and reference. The book should therefore be accessible to a wide spectrum of students and may also facilitate the transition between linear algebra and advanced functional analysis. Courses. The book is suitable for a one-semester course meeting five hours per week or for a two-semester course meeting three hours per week. The book can also be utilized for shorter courses. In fact, chapters can be omitted without destroying the continuity or making the rest of the book a torso (for details see below). For instance: Chapters 1 to 4 or 5 makes a very short course. Chapters 1 to 4 and 7 is a course that includes spectral theory and other topics.

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