LEADER 04078nam 22006375 450 001 9910845491303321 005 20240323111520.0 010 $a3-031-46320-X 024 7 $a10.1007/978-3-031-46320-4 035 $a(CKB)31094344000041 035 $a(MiAaPQ)EBC31227657 035 $a(Au-PeEL)EBL31227657 035 $a(DE-He213)978-3-031-46320-4 035 $a(EXLCZ)9931094344000041 100 $a20240323d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematics for Natural Scientists II$b[electronic resource] $eAdvanced Methods /$fby Lev Kantorovich 205 $a2nd ed. 2024. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2024. 215 $a1 online resource (944 pages) 225 1 $aUndergraduate Lecture Notes in Physics,$x2192-4805 311 $a3-031-46319-6 327 $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. 330 $aThis textbook, the second in a series (the first covered fundamentals and basics), seeks to make its material accessible to physics students. Physics/engineering can be greatly enhanced by knowledge of advanced mathematical techniques, but the math-specific jargon and laborious proofs can be off-putting to students not well versed in abstract math. This book uses examples and proofs designed to be clear and convincing from the context of physics, as well as providing a large number of both solved and unsolved problems in each chapter. This is the second edition, and it has been significantly revised and enlarged, with Chapters 1 (on linear algebra) and 2 (on the calculus of complex numbers and functions) having been particularly expanded. The enhanced topics throughout the book include: vector spaces, general (non-Hermitian, including normal and defective) matrices and their right/left eigenvectors/values, Jordan form, pseudoinverse, linear systems of differential equations, Gaussian elimination, fundamental theorem of algebra, convergence of a Fourie series and Gibbs-Wilbraham phenomenon, careful derivation of the Fourier integral and of the inverse Laplace transform. New material has been added on many physics topics meant to illustrate the maths, such as 3D rotation, properties of the free electron gas, van Hove singularities, and methods for both solving PDEs with a Fourier transform and calculating the width of a domain wall in a ferromagnet, to mention just a few. This textbook should prove invaluable to all of those with an interest in physics/engineering who have previously experienced difficulty processing the math involved. . 410 0$aUndergraduate Lecture Notes in Physics,$x2192-4805 606 $aMathematical physics 606 $aEngineering mathematics 606 $aEngineering$xData processing 606 $aChemometrics 606 $aMathematical Methods in Physics 606 $aMathematical and Computational Engineering Applications 606 $aMathematical Applications in Chemistry 606 $aMathematical Physics 606 $aTheoretical, Mathematical and Computational Physics 615 0$aMathematical physics. 615 0$aEngineering mathematics. 615 0$aEngineering$xData processing. 615 0$aChemometrics. 615 14$aMathematical Methods in Physics. 615 24$aMathematical and Computational Engineering Applications. 615 24$aMathematical Applications in Chemistry. 615 24$aMathematical Physics. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a530.15 700 $aKantorovich$b Lev$01065132 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910845491303321 996 $aMathematics for Natural Scientists II$92544348 997 $aUNINA