Techniques of Functional Analysis for Differential and Integral Equations

Erscheinungsjahr 2017
ISBN: 978-0-12-811426-1
Verlag: Elsevier Science

Buch, Englisch, 320 Seiten, Format (B × H): 150 mm x 226 mm, Gewicht: 522 g

Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given. The work provides many examples and exercises drawn from the literature.

Zielgruppe

<p>Graduate students and 1<SUP>st</SUP> year PhDs across applied mathematics, mathematics and in disciplines making use of applied mathematics. </p>

Autoren/Hrsg.

Sacks, Paul

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen

Inhaltsverzeichnis

1. Introduction2. Preliminaries3. Vector spaces4. Metric spaces5. Normed linear spaces and Banach spaces6. Inner product spaces and Hilbert spaces7. Distributions8. Fourier analysis and distributions9. Distributions and Differential Equations10. Linear operators11. Unbounded operators12. Spectrum of an operator13. Compact Operators14. Spectra and Green's functions for differential operators15. Further study of integral equations16. Variational methods17. Weak solutions of partial differential equations18. Appendices

Über Autor(innen)

Sacks, Paul
Professor Paul Sacks received his B.S. degree from Syracuse University and M.S. and Ph.D. degrees from the University of Wisconsin-Madison, all in Mathematics. Since 1981 he has been in the Mathematics department at Iowa State University, as Full Professor since 1990. He is particularly interested in partial differential equations and inverse problems. He is the author or co-author of more than 60 scientific articles and conference proceedings. For thirty years he has regularly taught courses in analysis, differential equations and methods of applied mathematics for mathematics graduate students.