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020 _a9783031603945
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024 7 _a10.1007/978-3-031-60394-5
_2doi
050 4 _aQC19.2-20.85
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
_2thema
100 1 _aDhurandhar, Sanjeev.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_980674
245 1 0 _aUnderstanding Mathematical Concepts in Physics
_h[electronic resource] :
_bInsights from Geometrical and Numerical Approaches /
_cby Sanjeev Dhurandhar.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXVI, 351 p. 57 illus., 42 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 _aLecture Notes in Physics,
_x1616-6361 ;
_v1030
505 0 _aDedication -- Preface -- Topology -- Hilbert Spaces -- Fourier Analysis -- Complex analysis: hands on -- Understanding differential equations: geometrical insights and general analysis -- Solving Differential Equations -- Differential Geometry and Tensors -- Representations of the rotation group and Lie groups -- Probability and Random Variables -- Probability distributions in physics -- The statistical detection of signals in noisy data -- Bibliography.
520 _aModern mathematics has become an essential part of today’s physicist’s arsenal and this book covers several relevant such topics. The primary aim of this book is to present key mathematical concepts in an intuitive way with the help of geometrical and numerical methods - understanding is the key. Not all differential equations can be solved with standard techniques. Examples illustrate how geometrical insights and numerical methods are useful in understanding differential equations in general but are indispensable when extracting relevant information from equations that do not yield to standard methods. Adopting a numerical approach to complex analysis it is shown that Cauchy’s theorem, the Cauchy integral formula, the residue theorem, etc. can be verified by performing hands-on computations with Python codes. Figures elucidate the concept of poles and essential singularities. Further the book covers topology, Hilbert spaces, Fourier transforms (discussing how fast Fourier transform works), modern differential geometry, Lie groups and Lie algebras, probability and useful probability distributions, and statistical detection of signals. Novel features include: (i) Topology is introduced via the notion of continuity on the real line which then naturally leads to topological spaces. (ii) Data analysis in a differential geometric framework and a general description of χ2 discriminators in terms of vector bundles. This book is targeted at physics graduate students and at theoretical (and possibly experimental) physicists. Apart from research students, this book is also useful to active physicists in their research and teaching.
650 0 _aMathematical physics.
650 0 _aMathematical analysis.
_964178
650 0 _aFourier analysis.
650 0 _aTopological groups.
_972299
650 0 _aLie groups.
_972300
650 0 _aDifferential equations.
650 1 4 _aTheoretical, Mathematical and Computational Physics.
_965563
650 2 4 _aMathematical Physics.
650 2 4 _aAnalysis.
650 2 4 _aFourier Analysis.
650 2 4 _aTopological Groups and Lie Groups.
_972304
650 2 4 _aDifferential Equations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031603938
776 0 8 _iPrinted edition:
_z9783031603952
776 0 8 _iPrinted edition:
_z9783031603969
830 0 _aLecture Notes in Physics,
_x1616-6361 ;
_v1030
_972070
856 4 0 _uhttps://doi.org/10.1007/978-3-031-60394-5
912 _aZDB-2-PHA
912 _aZDB-2-SXP
912 _aZDB-2-LNP
999 _c61650
_d61650