Analysis for Applied Mathematics

This textbook is designed for a course at the beginning graduate level, serving students of mathematics, engineering, physics, and other sciences. Its goal is to provide the analytical tools, concepts, and viewpoints needed for modern applied mathematics.

Provides analytical tools and concepts needed for solving problems in modern applied mathematics = core maths for applications Prepares readers for work in the modern theory of PDE's through coverage of the subjects of distributions Exercises in each chapter

Zusammenfassung
This book evolved from a course at our university for beginning graduate stu­ dents in mathematics-particularly students who intended to specialize in ap­ plied mathematics. The content of the course made it attractive to other math­ ematics students and to graduate students from other disciplines such as en­ gineering, physics, and computer science. Since the course was designed for two semesters duration, many topics could be included and dealt with in de­ 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 ap­ 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 ben­ 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.

Inhalt
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.