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020 _a9783031463204
_9978-3-031-46320-4
024 7 _a10.1007/978-3-031-46320-4
_2doi
050 4 _aQC19.2-20.85
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
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_2thema
100 1 _aKantorovich, Lev.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_973795
245 1 0 _aMathematics for Natural Scientists II
_h[electronic resource] :
_bAdvanced Methods /
_cby Lev Kantorovich.
250 _a2nd ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXXVII, 922 p. 127 illus., 121 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 _aUndergraduate Lecture Notes in Physics,
_x2192-4805
505 0 _aElements of linear algebra -- Complex numbers and functions -- Fourier series -- Special Functions -- Fourier Transform -- Laplace Transform -- Curvilinear coordinates -- Partial differential equations of mathematical physics -- Calculus of variations.
520 _aThis textbook, the second in a series (the first covered fundamentals and basics), seeks to make its material accessible to physics students. Physics/engineering can be greatly enhanced by knowledge of advanced mathematical techniques, but the math-specific jargon and laborious proofs can be off-putting to students not well versed in abstract math. This book uses examples and proofs designed to be clear and convincing from the context of physics, as well as providing a large number of both solved and unsolved problems in each chapter. This is the second edition, and it has been significantly revised and enlarged, with Chapters 1 (on linear algebra) and 2 (on the calculus of complex numbers and functions) having been particularly expanded. The enhanced topics throughout the book include: vector spaces, general (non-Hermitian, including normal and defective) matrices and their right/left eigenvectors/values, Jordan form, pseudoinverse, linear systems of differential equations, Gaussian elimination, fundamental theorem of algebra, convergence of a Fourie series and Gibbs-Wilbraham phenomenon, careful derivation of the Fourier integral and of the inverse Laplace transform. New material has been added on many physics topics meant to illustrate the maths, such as 3D rotation, properties of the free electron gas, van Hove singularities, and methods for both solving PDEs with a Fourier transform and calculating the width of a domain wall in a ferromagnet, to mention just a few. This textbook should prove invaluable to all of those with an interest in physics/engineering who have previously experienced difficulty processing the math involved. .
650 0 _aMathematical physics.
650 0 _aEngineering mathematics.
_964145
650 0 _aEngineering
_xData processing.
650 0 _aChemometrics.
_973553
650 1 4 _aMathematical Methods in Physics.
_970877
650 2 4 _aMathematical and Computational Engineering Applications.
650 2 4 _aMathematical Applications in Chemistry.
_973555
650 2 4 _aMathematical Physics.
650 2 4 _aTheoretical, Mathematical and Computational Physics.
_965563
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031463198
776 0 8 _iPrinted edition:
_z9783031463211
830 0 _aUndergraduate Lecture Notes in Physics,
_x2192-4805
_973796
856 4 0 _uhttps://doi.org/10.1007/978-3-031-46320-4
912 _aZDB-2-PHA
912 _aZDB-2-SXP
999 _c58592
_d58592