04180nam a22005895i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001700186072001600203072002300219072002300242082001400265100003100279245013300310264004200443300004300485336002600528337002600554338003600580347002400616490004400640505030000684520189800984650001702882650002202899650002502921650002302946650002502969650001302994650002503007650002903032650001703061650005403078650002203132650002503154650005903179650003703238650002303275710003403298773002003332776003603352830004403388856004803432912001403480999001903494952007703513978-0-8176-4980-7DE-He21320180115171442.0cr nn 008mamaa100528s2010 xxu| s |||| 0|eng d a97808176498079978-0-8176-4980-77 a10.1007/978-0-8176-4980-72doi 4aTA342-343 7aPBWH2bicssc 7aTBJ2bicssc 7aMAT0030002bisacsh 7aTEC0090602bisacsh04a003.32231 aChristensen, Ole.eauthor.10aFunctions, Spaces, and Expansionsh[electronic resource] :bMathematical Tools in Physics and Engineering /cby Ole Christensen. 1aBoston :bBirkhäuser Boston,c2010. aXIX, 266 p. 9 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aApplied and Numerical Harmonic Analysis0 aMathematical Background -- Normed Vector Spaces -- Banach Spaces -- Hilbert Spaces -- The Lp-spaces -- The Hilbert Space L2 -- The Fourier Transform -- An Introduction to Wavelet Analysis -- A Closer Look at Multiresolution Analysis -- B-splines -- Special Functions -- Appendix A -- Appendix B. aThis graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically chosen because it plays a key role outside the field of pure mathematics. Although the treatment of each topic is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are fundamental to exploring the computational aspects of physics and engineering. A central theme of the book is the structure of various vector spaces—most importantly, Hilbert spaces—and expansions of elements in these spaces in terms of bases. Key topics and features include: * More than 150 exercises * Abstract and normed vector spaces * Approximation in normed vector spaces * Hilbert and Banach spaces * General bases and orthonormal bases * Linear operators on various normed spaces * The Fourier transform, including the discrete Fourier transform * Wavelets and multiresolution analysis * B-splines * Sturm–Liouville problems As a textbook that provides a deep understanding of central issues in mathematical analysis, Functions, Spaces, and Expansions is intended for graduate students, researchers, and practitioners in applied mathematics, physics, and engineering. Readers are expected to have a solid understanding of linear algebra, in Rn and in general vector spaces. Familiarity with the basic concepts of calculus and real analysis, including Riemann integrals and infinite series of real or complex numbers, is also required. Functions, Spaces, and Expansions is the main textbook for the e-course Mathematics 4: Real Analysis currently being taught at the Technical University of Denmark. Please click the "Course Materials" link on the right to access videos of the lectures, problem sheets, and solutions to selected exercises. 0aMathematics. 0aFourier analysis. 0aFunctional analysis. 0aSpecial functions. 0aMathematical models. 0aPhysics. 0aApplied mathematics. 0aEngineering mathematics.14aMathematics.24aMathematical Modeling and Industrial Mathematics.24aFourier Analysis.24aFunctional Analysis.24aAppl.Mathematics/Computational Methods of Engineering.24aMathematical Methods in Physics.24aSpecial Functions.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780817649791 0aApplied and Numerical Harmonic Analysis40uhttp://dx.doi.org/10.1007/978-0-8176-4980-7 aZDB-2-SMA c370054d370054 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK