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Understanding mathematical concepts in physics = insights from geometrical and numerical approaches /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Understanding mathematical concepts in physics/ by Sanjeev Dhurandhar.
其他題名:	insights from geometrical and numerical approaches /
作者:	Dhurandhar, Sanjeev.
出版者:	Cham :Springer Nature Switzerland : : 2024.,
面頁冊數:	xvi, 351 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Differential Equations. -
電子資源:	https://doi.org/10.1007/978-3-031-60394-5
ISBN:	9783031603945

Understanding mathematical concepts in physics = insights from geometrical and numerical approaches /
Dhurandhar, Sanjeev.

Understanding mathematical concepts in physicsinsights from geometrical and numerical approaches /[electronic resource] :by Sanjeev Dhurandhar. - Cham :Springer Nature Switzerland :2024. - xvi, 351 p. :ill. (some col.), digital ;24 cm. - Lecture notes in physics,v. 10301616-6361 ;. - Lecture notes in physics ;777 .

Dedication -- 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.

Modern 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.

ISBN: 9783031603945

Standard No.: 10.1007/978-3-031-60394-5doiSubjects--Topical Terms:

681826
Differential Equations.

LC Class. No.: QC20

Dewey Class. No.: 530.15

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