Continuous Functions

Inbunden, Engelska, 2020

1 721 kr

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Beskrivning

This book is the second of a set dedicated to the mathematical tools used in partial differential equations derived from physics. It presents the properties of continuous functions, which are useful for solving partial differential equations, and, more particularly, for constructing distributions valued in a Neumann space. The author examines partial derivatives, the construction of primitives, integration and the weighting of value functions in a Neumann space. Many of them are new generalizations of classical properties for values in a Banach space. Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students – doctoral students, postgraduate students – engineers and researchers, without restricting or generalizing the results.

Produktinformation

Utgivningsdatum:2020-11-24
Mått:10 x 10 x 10 mm
Vikt:454 g
Format:Inbunden
Språk:Engelska
Antal sidor:272
Förlag:ISTE Ltd and John Wiley & Sons Inc
ISBN:9781786300102

Utforska kategorier

Tillämpad matematik inom Naturvetenskap och teknik

Mer om författaren

Jacques Simon is Honorary Research Director at CNRS. His research focuses on Navier-Stokes equations, particularly in shape optimization and in the functional spaces they use.

Innehållsförteckning

Introduction ixFamiliarization with Semi-normed Spaces xiiiNotations xvChapter 1. Spaces of Continuous Functions 11.1. Notions of continuity 11.2. Spaces C(Ω;E), Cb(Ω;E), CK(Ω;E), C(Ω;E) and Cb(Ω;E) 31.3. Comparison of spaces of continuous functions 61.4. Sequential completeness of spaces of continuous functions 101.5. Metrizability of spaces of continuous functions 111.6. The space K(Ω;E) 141.7. Continuous mappings 201.8. Continuous extension and restriction 221.9. Separation and permutation of variables 231.10. Sequential compactness in Cb(Ω;E) 28Chapter 2. Differentiable Functions 312.1. Differentiability 312.2. Finite increment theorem 342.3. Partial derivatives 372.4. Higher order partial derivatives 402.5. Spaces Cm(Ω;E), Cmb(Ω;E), CmK