001453774 000__ 04474cam\a22005777i\4500
001453774 001__ 1453774
001453774 003__ OCoLC
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001453774 019__ $$a1356798189$$a1356798346$$a1357018833
001453774 020__ $$a9783031133794$$qelectronic book
001453774 020__ $$a303113379X$$qelectronic book
001453774 020__ $$z9783031133787
001453774 020__ $$z3031133781
001453774 0247_ $$a10.1007/978-3-031-13379-4$$2doi
001453774 035__ $$aSP(OCoLC)1357149359
001453774 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dEBLCP$$dYDX$$dOCLCQ$$dYDX$$dUKAHL
001453774 0411_ $$aeng$$hger
001453774 049__ $$aISEA
001453774 050_4 $$aQA374$$b.A74 2022
001453774 08204 $$a515/.353$$223/eng/20230109
001453774 1001_ $$aArendt, Wolfgang,$$d1950-$$eauthor.$$1https://isni.org/isni/0000000114456795
001453774 24010 $$aPartielle Differenzialgleichungen.$$lEnglish
001453774 24510 $$aPartial differential equations :$$ban introduction to analytical and numerical methods /$$cWolfgang Arendt, Karsten Urban ; translated from the German by James B. Kennedy.
001453774 24630 $$aIntroduction to analytical and numerical methods
001453774 264_1 $$aCham :$$bSpringer,$$c2022.
001453774 300__ $$a1 online resource (1 volume) :$$billustrations (black and white)
001453774 336__ $$atext$$btxt$$2rdacontent
001453774 337__ $$acomputer$$bc$$2rdamedia
001453774 338__ $$aonline resource$$bcr$$2rdacarrier
001453774 4901_ $$aGraduate texts in mathematics ;$$v294
001453774 500__ $$aTranslated from the German.
001453774 504__ $$aIncludes bibliographical references.
001453774 5050_ $$a1 Modeling, or where do differential equations come from -- 2 Classification and characteristics -- 3 Elementary methods -- 4 Hilbert spaces -- 5 Sobolev spaces and boundary value problems in dimension one -- 6 Hilbert space methods for elliptic equations -- 7 Neumann and Robin boundary conditions -- 8 Spectral decomposition and evolution equations -- 9 Numerical methods -- 10 Maple, or why computers can sometimes help -- Appendix.
001453774 506__ $$aAccess limited to authorized users.
001453774 520__ $$aThis textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses on finite difference and finite element methods. Computer-aided calculation with Maple completes the book. Throughout, three fundamental examples are studied with different tools: Poissons equation, the heat equation, and the wave equation on Euclidean domains. The BlackScholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed.
001453774 588__ $$aDescription based on print version record.
001453774 650_0 $$aDifferential equations, Partial.
001453774 655_0 $$aElectronic books.
001453774 7001_ $$aUrban, Karsten,$$eauthor.$$1https://isni.org/isni/0000000117460677
001453774 7001_ $$aKennedy, J. B.,$$etranslator.
001453774 77608 $$iPrint version:$$aArendt, Wolfgang, 1950-$$tPartial differential equations.$$dCham : Springer, 2022$$z9783031133787$$w(OCoLC)1346496719
001453774 830_0 $$aGraduate texts in mathematics ;$$v294.
001453774 852__ $$bebk
001453774 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-13379-4$$zOnline Access$$91397441.1
001453774 909CO $$ooai:library.usi.edu:1453774$$pGLOBAL_SET
001453774 980__ $$aBIB
001453774 980__ $$aEBOOK
001453774 982__ $$aEbook
001453774 983__ $$aOnline
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