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Mathematics for natural scientists.advanced methods /II

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Mathematics for natural scientists.by Lev Kantorovich.
其他題名:	advanced methods /
作者:	Kantorovich, Lev.
出版者:	Cham :Springer International Publishing :2024.
面頁冊數:	xxvii, 922 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Mathematical physics.
電子資源:	https://doi.org/10.1007/978-3-031-46320-4
ISBN:	9783031463204$q(electronic bk.)

Mathematics for natural scientists.advanced methods /II
Kantorovich, Lev.

Mathematics for natural scientists.advanced methods /II[electronic resource] :by Lev Kantorovich. - Second edition. - Cham :Springer International Publishing :2024. - xxvii, 922 p. :ill. (some col.), digital ;24 cm. - Undergraduate lecture notes in physics,2192-4805. - Undergraduate lecture notes in physics..

Elements 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.

This 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.

ISBN: 9783031463204$q(electronic bk.)

Standard No.: 10.1007/978-3-031-46320-4doiSubjects--Topical Terms:

190854
Mathematical physics.

LC Class. No.: QC20

Dewey Class. No.: 530.15

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