03706nam a22004815i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001700153072001600170072002300186072001500209100007900224245010800303250001800411264006900429300006900498336002600567337002600593338003600619347002400655490005500679505025700734520166800991650002602659650002902685650003402714650001802748650003702766650006102803650004402864650002602908650005702934710003402991773002603025776003603051776003603087830005503123856004603178978-3-031-46320-4DE-He21320251030111740.0cr nn 008mamaa240323s2024    sz |    s    |||| 0|eng d  a97830314632047 a10.1007/978-3-031-46320-42doi 4aQC19.2-20.85 7aPHU2bicssc 7aSCI0400002bisacsh 7aPHU2thema1 aKantorovich, Lev.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aMathematics for Natural Scientists IIh[electronic resource] :bAdvanced Methods /cby Lev Kantorovich.  a2nd ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXXVII, 922 p. 127 illus., 121 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aUndergraduate Lecture Notes in Physics,x2192-48050 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.  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. . 0aMathematical physics. 0aEngineering mathematics. 0aEngineeringxData processing. 0aChemometrics.14aMathematical Methods in Physics.24aMathematical and Computational Engineering Applications.24aMathematical Applications in Chemistry.24aMathematical Physics.24aTheoretical, Mathematical and Computational Physics.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303146319808iPrinted edition:z9783031463211 0aUndergraduate Lecture Notes in Physics,x2192-480540uhttps://doi.org/10.1007/978-3-031-46320-4