Functional analysis for physics and engineering : an introduction /: an introduction. (2015)
- Record Type:
- Book
- Title:
- Functional analysis for physics and engineering : an introduction /: an introduction. (2015)
- Main Title:
- Functional analysis for physics and engineering : an introduction
- Further Information:
- Note: Hiroyuki Shima.
- Authors:
- Shima, Hiroyuki, 1975-
- Contents:
- Prologue What Functional Analysis tells us From perspective of the limit From perspective of infinite dimension From perspective of quantum mechanical theory Topology Fundamentals Continuous mapping Homeomorphism Vector space What is vector space? Property of vector space Hierarchy of vector space Hilbert space Basis and completeness Equivalence of L 2 spaces with ℓ 2 spaces Tensor space Two faces of one tensor "Vector" as a linear function Tensor as a multilinear function Component of tensor Lebesgue integral Motivation & Merits Measure theory Lebesgue integral Lebesgue convergence theorem Lp space Wavelet Continuous wavelet analysis Discrete wavelet analysis Wavelet space Distribution Motivation & Merits Establishing the concept of distribution Examples of distribution Mathematical manipulation of distribution Completion Completion of number space Sobolev space Operator Classification of operators Essence of operator theory Preparation toward eigenvalue-like problem Practical importance of non-continuous operators Real number sequence A.1 Convergence of real sequence A.2 Bounded sequence A.3 Uniqueness of the limit of real sequence Cauchy sequence B.1 What is Cauchy sequence? B.2 Cauchy criterion for real number sequence Real number series C.1 Limit of real number series C.2 Cauchy criterion for real number series Continuity and smoothness of function D.1 Limit of function D.2 Continuity of function D.3 Derivative of function D.4 Smooth function Function sequence E.1Prologue What Functional Analysis tells us From perspective of the limit From perspective of infinite dimension From perspective of quantum mechanical theory Topology Fundamentals Continuous mapping Homeomorphism Vector space What is vector space? Property of vector space Hierarchy of vector space Hilbert space Basis and completeness Equivalence of L 2 spaces with ℓ 2 spaces Tensor space Two faces of one tensor "Vector" as a linear function Tensor as a multilinear function Component of tensor Lebesgue integral Motivation & Merits Measure theory Lebesgue integral Lebesgue convergence theorem Lp space Wavelet Continuous wavelet analysis Discrete wavelet analysis Wavelet space Distribution Motivation & Merits Establishing the concept of distribution Examples of distribution Mathematical manipulation of distribution Completion Completion of number space Sobolev space Operator Classification of operators Essence of operator theory Preparation toward eigenvalue-like problem Practical importance of non-continuous operators Real number sequence A.1 Convergence of real sequence A.2 Bounded sequence A.3 Uniqueness of the limit of real sequence Cauchy sequence B.1 What is Cauchy sequence? B.2 Cauchy criterion for real number sequence Real number series C.1 Limit of real number series C.2 Cauchy criterion for real number series Continuity and smoothness of function D.1 Limit of function D.2 Continuity of function D.3 Derivative of function D.4 Smooth function Function sequence E.1 Pointwise convergence E.2 Uniform convergence E.3 Cauchy criterion for function series F Uniformly convergent sequence of functions F.1 Continuity of the limit function F.2 Integrability of the limit function F.3 Differentiability of the limit function G Function series G.1 Infinite series of functions G.2 Properties of uniformly convergent series of functions H Matrix eigenvalue problem H.1 Eigenvalue and eigenvector H.2 Hermite matrix I Eigenspace decomposition I.1 Eigenspace of matrix I.2 Direct sum decomposition Index … (more)
- Edition:
- 1st
- Publisher Details:
- Boca Raton : CRC Press
- Publication Date:
- 2015
- Extent:
- 1 online resource, illustrations (black and white)
- Subjects:
- 515.702462
Functional analysis
Engineering mathematics
Mathematical physics - Languages:
- English
- ISBNs:
- 9781482223033
- Related ISBNs:
- 9781482223019
- Notes:
- Note: Description based on CIP data; item not viewed.
- Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.138300
- Ingest File:
- 02_007.xml