This book evolved from a course at our university for beginning graduate stuยญ dents in mathematics-particularly students who intended to specialize in apยญ plied mathematics. The content of the course made it attractive to other mathยญ ematics students and to graduate students from other disciplines such as enยญ gineering, physics, and computer science. Since the course was designed for two semesters duration, many topics could be included and dealt with in deยญ tail. Chapters 1 through 6 reflect roughly the actual nature of the course, as it was taught over a number of years. The content of the course was dictated by a syllabus governing our preliminary Ph. D. examinations in the subject of apยญ plied mathematics. That syllabus, in turn, expressed a consensus of the faculty members involved in the applied mathematics program within our department. The text in its present manifestation is my interpretation of that syllabus: my colleagues are blameless for whatever flaws are present and for any inadvertent deviations from the syllabus. The book contains two additional chapters having important material not included in the course: Chapter 8, on measure and integration, is for the benยญ efit of readers who want a concise presentation of that subject, and Chapter 7 contains some topics closely allied, but peripheral, to the principal thrust of the course. This arrangement of the material deserves some explanation
CONTENT
1 Normed Linear Spaces -- 2 Hilbert Spaces -- 3 Calculus in Banach Spaces -- 4 Basic Approximate Methods of Analysis -- 5 Distributions -- 6 The Fourier Transform -- 7 Additional Topics -- 8 Measure and Integration -- References -- Symbols
