000			05548cam a2200625Mu 4500
001			9780429343315
003			FlBoTFG
005			20220414100114.0
006			m o d
007			cr |||||||||||
008			200912s2020 xx o 000 0 eng d
040			_aOCoLC-P _beng _epn _cOCoLC-P
020			_a9781000205879
020			_a1000205878
020			_a9781000205893 _q(ePub ebook)
020			_a1000205894
020			_a9781000205886 _q(Mobipocket ebook)
020			_a1000205886
020			_a9780429343315 _q(ebook)
020			_a0429343310
020			_z9780367356743
020			_z0367356740
024	7		_a10.1201/9780429343315 _2doi
035			_a(OCoLC)1193130373 _z(OCoLC)1191239474 _z(OCoLC)1196191988
035			_a(OCoLC-P)1193130373
050		4	_aQA320
072		7	_aMAT _x037000 _2bisacsh
072		7	_aSCI _x040000 _2bisacsh
072		7	_aMAT _x000000 _2bisacsh
072		7	_aPBKF _2bicssc
082	0	4	_a515.64 _223
100	1		_aBotelho, Fabio Silva.
245	1	0	_aFunctional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering
260			_aMilton : _bTaylor & Francis Group, _c2020.
300			_a1 online resource (589 pages)
336			_atext _btxt _2rdacontent
336			_astill image _bsti _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
505	0		_aCover -- Title Page -- Copyright Page -- Preface -- Acknowledgements -- Table of Contents -- Section I: Functional Analysis -- 1. Metric Spaces -- 1.1 Introduction -- 1.2 The main definitions -- 1.2.1 The space l
505	8		_a1.5 The Arzela-Ascoli theorem -- 2. Topological Vector Spaces -- 2.1 Introduction -- 2.2 Vector spaces -- 2.3 Some properties of topological vector spaces -- 2.3.1 Nets and convergence -- 2.4 Compactness in topological vector spaces -- 2.4.1 A note on convexity in topological vector spaces -- 2.5 Normed and metric spaces -- 2.6 Linear mappings -- 2.7 Linearity and continuity -- 2.8 Continuity of operators in Banach spaces -- 2.9 Some classical results on Banach spaces -- 2.9.1 The Baire Category theorem -- 2.9.2 The Principle of Uniform Boundedness -- 2.9.3 The Open Mapping theorem
505	8		_a2.9.4 The Closed Graph theorem -- 2.10 A note on finite dimensional normed spaces -- 3. Hilbert Spaces -- 3.1 Introduction -- 3.2 The main definitions and results -- 3.3 Orthonormal basis -- 3.3.1 The Gram-Schmidt orthonormalization -- 3.4 Projection on a convex set -- 3.5 The theorems of Stampacchia and Lax-Milgram -- 4. The Hahn-Banach Theorems and the Weak Topologies -- 4.1 Introduction -- 4.2 The Hahn-Banach theorems -- 4.3 The weak topologies -- 4.4 The weak-star topology -- 4.5 Weak-star compactness -- 4.6 Separable sets -- 4.7 Uniformly convex spaces -- 5. Topics on Linear Operators
505	8		_a5.1 Topologies for bounded operators -- 5.2 Adjoint operators -- 5.3 Compact operators -- 5.4 The square root of a positive operator -- 6. Spectral Analysis, a General Approach in Normed Spaces -- 6.1 Introduction -- 6.2 Sesquilinear functionals -- 6.3 About the spectrum of a linear operator defined on a banach space -- 6.4 The spectral theorem for bounded self-adjoint operators -- 6.4.1 The spectral theorem -- 6.5 The spectral decomposition of unitary transformations -- 6.6 Unbounded operators -- 6.6.1 Introduction -- 6.7 Symmetric and self-adjoint operators
505	8		_a6.7.1 The spectral theorem using Cayley transform -- 7. Basic Results on Measure and Integration -- 7.1 Basic concepts -- 7.2 Simple functions -- 7.3 Measures -- 7.4 Integration of simple functions -- 7.5 Signed measures -- 7.6 The Radon-Nikodym theorem -- 7.7 Outer measure and measurability -- 7.8 Fubini's theorem -- 7.8.1 Product measures -- 8. The Lebesgue Measure in Rn -- 8.1 Introduction -- 8.2 Properties of the outer measure -- 8.3 The Lebesgue measure -- 8.4 Outer and inner approximations of Lebesgue measurable sets -- 8.5 Some other properties of measurable sets
500			_a8.6 Lebesgue measurable functions
520			_aThe book discusses basic concepts of functional analysis, measure and integration theory, calculus of variations and duality and its applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism and others. Numerical Methods for such and similar problems, such as models in flight mechanics and the Navier-Stokes system in fluid mechanics have been developed through the generalized method of lines, including their matrix finite dimensional approximations. It concludes with a review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity. The book will be of interest to applied mathematicians and graduate students in applied mathematics. Physicists, engineers and researchers in related fields will also find the book useful in providing a mathematical background applicable to their respective professional areas.
588			_aOCLC-licensed vendor bibliographic record.
650		0	_aCalculus of variations.
650		0	_aFunctional analysis.
650		7	_aMATHEMATICS _xFunctional Analysis. _2bisacsh
650		7	_aSCIENCE _xMathematical Physics. _2bisacsh
650		7	_aMATHEMATICS _xGeneral. _2bisacsh
856	4	0	_3Taylor & Francis _uhttps://www.taylorfrancis.com/books/e/9780429343315
856	4	2	_3OCLC metadata license agreement _uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
999			_c55724 _d55724