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008 170112s2016 gw | s |||| 0|eng d
020 _a9783319489360
_9978-3-319-48936-0
024 7 _a10.1007/978-3-319-48936-0
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
082 0 4 _a515.353
_223
100 1 _aBorthwick, David.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aIntroduction to Partial Differential Equations
_h[electronic resource] /
_cby David Borthwick.
250 _a1st ed. 2016.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2016.
300 _aXVI, 283 p. 68 illus., 61 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext,
_x0172-5939
505 0 _a1. Introduction -- 2. Preliminaries -- 3. Conservation Equations and Characteristics -- 4. The Wave Equation -- 5. Separation of Variables -- 6. The Heat Equation -- 7. Function Spaces -- 8. Fourier Series -- 9. Maximum Principles -- 10. Weak Solutions -- 11. Variational Methods -- 12. Distributions -- 13. The Fourier Transform -- A. Appendix: Analysis Foundations -- References -- Notation Guide -- Index.
520 _aThis modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions: (1) What is the scientific problem we are trying to understand? (2) How do we model that with PDE? (3) What techniques can we use to analyze the PDE? (4) How do those techniques apply to this equation? (5) What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.
650 0 _aPartial differential equations.
650 0 _aMathematical physics.
650 1 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aMathematical Applications in the Physical Sciences.
_0http://scigraph.springernature.com/things/product-market-codes/M13120
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319489346
776 0 8 _iPrinted edition:
_z9783319489353
776 0 8 _iPrinted edition:
_z9783319840512
830 0 _aUniversitext,
_x0172-5939
856 4 0 _uhttps://doi.org/10.1007/978-3-319-48936-0
912 _aZDB-2-SMA
999 _c17965
_d17965
942 _cebook