Tensor Trigonometry
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Tensor Trigonometry
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Author : Ninul A.S.
language : en
Publisher: Fizmatkniga
Release Date :
Tensor Trigonometry written by Ninul A.S. and has been published by Fizmatkniga this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
The Tensor Trigonometry, with revealing a tensor nature of the angles and their functions and added by differential trigonometry, is developed for wide applications in various fields. Planimetry includes metric part and trigonometry. In geometries of metric spaces from the end of XIX age their tensor forms are widely used. Trigonometry was remaining in its scalar flat forms. Tensor Trigonometry is its development from Leonard Euler classic forms into spatial k-dimensional (at k > 2) tensor forms with vector and scalar orthoprojections, with step by step increasing a complexity and opportunities. Described in the book are fundamentals of this new mathematical subject with many initial examples of applications. In theoretic plan, Tensor Trigonometry complements naturally Analytic Geometry and Linear Algebra. In practical plan, it gives the clear tools for analysis and solutions of various geometric and physical problems in homogeneous isotropic spaces, as Euclidean, quasi- and pseudo-Euclidean ones, on perfect surfaces of constant radius embedded into them with n-D non-Euclidean Geometries, and in Theory of Relativity. So, it gives classic projective models of non-Euclidean Geometries as trigonometric ones, general laws of summing two-steps and polysteps motions in complete differential and integral forms with polar decomposition of the sum into principal and induced orthospherical motions. The applications were developed till the differential tensor trigonometry of world lines and curves in 3D and 4D pseudo- and quasi- Euclidean spaces, in addition, to the classic Frenet-Serret theory, with absolute and relative differential-geometric parameters of curves, main kinematic and dynamical characteristics of a body moving in space-time along a world line with 4-velocity of Poincare. Due to our tensor trigonometric approach, clear explanations of all well-known and new STR and GR relativistic effects are given with physical interpretations in full agreement with the Law of Energy-Momentum conservation, Quantum Mechanics, Noether Theorem and Higgs Theory. The Tensor Trigonometry can be useful in various domains of mathematics and physics. It is intended to researchers in the fields of analytic geometry of any dimension, linear algebra with matrix theory, non-Euclidean geometries, theory of relativity, quantum mechanics and to all those who is interested in new knowledges and applications, given by exact sciences. It may be useful for educational purposes with this new math subject in the university and graduate schools departments of algebra, geometry and physics - relativistic and classical. The 1st edition of the Tensor Trigonometry was published by the main Russian scientific publishing house "MIR" in October 2004 - ISBN 10: 5030037179 (for instance, A. S. Ninul "Tenzornaja trigonometrija" in SUB.Uni-Goettingen.de and WorldCat OCLC 255128609). It was reviewed by the Moscow State University professor, Dr.Sc. M. M. Postnikov and by the Moscow Regional University professor, Dr.Sc. О. V. Manturov. This 3rd edition is a renovation of previous two in 2004) (by MIR) and in 2021 (by Fizmatlit).
Tensor Trigonometry
DOWNLOAD
Author : Ninul A.S.
language : en
Publisher: Fizmatkniga
Release Date :
Tensor Trigonometry written by Ninul A.S. and has been published by Fizmatkniga this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
The Tensor Trigonometry, with revealing a tensor nature of the angles and their functions and added by differential trigonometry, is developed for wide applications in various fields. Planimetry includes metric part and trigonometry. In geometries of metric spaces from the end of XIX age their tensor forms are widely used. Trigonometry was remaining in its scalar flat forms. Tensor Trigonometry is its development from Leonard Euler classic forms into spatial k-dimensional (at k > 2) tensor forms with vector and scalar orthoprojections, with step by step increasing a complexity and opportunities. Described in the book are fundamentals of this new mathematical subject with many initial examples of applications. In theoretic plan, Tensor Trigonometry complements naturally Analytic Geometry and Linear Algebra. In practical plan, it gives the clear tools for analysis and solutions of various geometric and physical problems in homogeneous isotropic spaces, as Euclidean, quasi- and pseudo-Euclidean ones, on perfect surfaces of constant radius embedded into them with n-D non-Euclidean Geometries, and in Theory of Relativity. So, it gives classic projective models of non-Euclidean Geometries as trigonometric ones, general laws of summing two-steps and polysteps motions in complete differential and integral forms with polar decomposition of the sum into principal and induced orthospherical motions. The applications were developed till the differential tensor trigonometry of world lines and curves in 3D and 4D pseudo- and quasi- Euclidean spaces, in addition, to the classic Frenet-Serret theory, with absolute and relative differential-geometric parameters of curves, main kinematic and dynamical characteristics of a body moving in space-time along a world line with 4-velocity of Poincare. Due to our tensor trigonometric approach, clear explanations of all well-known and new STR and GR relativistic effects are given with physical interpretations in full agreement with the Law of Energy-Momentum conservation, Quantum Mechanics, Noether Theorem and Higgs Theory. The Tensor Trigonometry can be useful in various domains of mathematics and physics. It is intended to researchers in the fields of analytic geometry of any dimension, linear algebra with matrix theory, non-Euclidean geometries, theory of relativity, quantum mechanics and to all those who is interested in new knowledges and applications, given by exact sciences. It may be useful for educational purposes with this new math subject in the university and graduate schools departments of algebra, geometry and physics - relativistic and classical. The 1st edition of the Tensor Trigonometry was published by the main Russian scientific publishing house "MIR" in October 2004 - ISBN 10: 5030037179 (for instance, A. S. Ninul "Tenzornaja trigonometrija" in SUB.Uni-Goettingen.de and WorldCat OCLC 255128609). It was reviewed by the Moscow State University professor, Dr.Sc. M. M. Postnikov and by the Moscow Regional University professor, Dr.Sc. О. V. Manturov. This 3rd edition is a renovation of previous two in 2004) (by MIR) and in 2021 (by Fizmatlit).
The Algebra Of Coplanar Vectors And Trigonometry
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Author : Robert Baldwin Hayward
language : en
Publisher:
Release Date : 1892
The Algebra Of Coplanar Vectors And Trigonometry written by Robert Baldwin Hayward and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1892 with Exponential functions categories.
Schaum S Outline Of Trigonometry
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Author : Robert E. Moyer
language : en
Publisher: McGraw Hill Professional
Release Date : 1998-12-21
Schaum S Outline Of Trigonometry written by Robert E. Moyer and has been published by McGraw Hill Professional this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-21 with Mathematics categories.
Updated to match the emphasis in today's courses, this clear study guide focuses entirely on plane trigonometry. It summarizes the geometry properties and theorems that prove helpful for solving trigonometry problems. Also, where solving problems requires knowledge of algebra, the algebraic processes and the basic trigonometric relations are explained carefully. Hundreds of problems solved step by step speed comprehension, make important points memorable, and teach problem-solving skills. Many additional problems with answers help reinforce learning and let students gauge their progress as they go.
Requirements In The Field Of Geology
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Author : Robert Grier Reeves
language : en
Publisher:
Release Date : 1970
Requirements In The Field Of Geology written by Robert Grier Reeves and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Earth sciences categories.
Vector And Tensor Analysis With Applications
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Author : A. I. Borisenko
language : en
Publisher: Courier Corporation
Release Date : 2012-08-28
Vector And Tensor Analysis With Applications written by A. I. Borisenko and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-28 with Mathematics categories.
Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.
Mathematics Dictionary
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Author : R.C. James
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-07-31
Mathematics Dictionary written by R.C. James and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-07-31 with Mathematics categories.
For more than 50 years, this classic reference has provided fundamental data in an accessible, concise form. This edition of the Mathematics Dictionary incorporates updated terms and concepts in its span of more than 8,000 topics from a broad spectrum of mathematical specialties. It features review-length descriptions of theories, practices and principles as well as a multilingual index.
Atmospheric Lidar Fundamentals
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Author : Chiao-Yao She
language : en
Publisher: Cambridge University Press
Release Date : 2022-03-03
Atmospheric Lidar Fundamentals written by Chiao-Yao She and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-03 with Science categories.
A comprehensive treatment of the essential physics of light-matter interactions and the fundamentals of atmospheric lidars.
Vector And Tensor Analysis
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Author : Louis Brand
language : en
Publisher:
Release Date : 1947
Vector And Tensor Analysis written by Louis Brand and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1947 with Calculus of tensors categories.
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Author : Нинул Анатолий Сергеевич
language : ru
Publisher: Мир
Release Date : 2004-10-04
written by Нинул Анатолий Сергеевич and has been published by Мир this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-04 with Mathematics categories.
Главные цели данной монографии – развить ряд геометрических понятий теории точных матриц и далее разработать главные положения тензорной тригонометрии для бивалентных тензорных углов, образуемых линейными подпространствами или связанных с их вращением. В первом разделе (главы 1–4) рассмотрен ряд вопросов теории точных матриц. Сформулировано генеральное неравенство для средних величин, на основе которого установлены иерархические инварианты для спектрально положительной матрицы. Выражены в явном виде собственные проекторы и квазиобратные матрицы – через коэффициенты характеристического многочлена. Идентифицирован минимальный аннулирующий многочлен. Изучены параметры сингулярности матриц и связанные с ними неравенства. Определены нуль-простые и нуль-нормальные сингулярные матрицы. Во втором разделе (главы 5–12) развита тензорная тригонометрия в аффинной и метрической формах. Определены бинарные угловые и модульные характеристики линейных объектов. Построена квазиевклидова и псевдоевклидова тензорная тригонометрия в трёх видах: проективная, рефлективная и моторная (последняя – ротационная или деформационная). Установлен тригонометрический спектр нуль-простой матрицы, на основе которого получены генеральные нормирующие синусное и косинусное неравенства. Определены квадратичные нормы матриц. В Приложении тензорная тригонометрия в своих элементарных формах используется для изучения движений в неевклидовых геометриях и в теории относительности. Для суммирования в них двух и многоступенчатых движений (скоростей) применено полярное представление тригонометрических ротаций. Закону суммирования движений (скоростей) придана генеральная матричная форма. Реализована гиперболическая формализация эйнштейнова замедления времени и лоренцева сокращения протяжённости как следствий ротационного и деформационного преобразований координат. Даны формулы вычисления и тригонометрическая интерпретация вторичной ортосферической ротации. Предложены тригонометрические модели для релятивистской кинематики и динамики материальной точки в пространстве-времени Минковского. Рассмотрены четыре абсолютные векторные и скалярные дифференциально-геометрические и физические характеристики кривой мировой линии, полностью определяющие её конфигурацию и конформацию в окрестности каждой собственной мировой точки, как 4D тензорно тригонометрический псевдоаналог 3D классической теории Френе-Серре в Евклидовом пространстве. В бумажной форме эту книгу, не имея её, можно посмотреть в больших научных библиотеках - российских и зарубежных. Например, в Евросоюзе – в наиболее известной и престижной европейской математической библиотеке Zentral Universitätsbibliothek Göttingen, как книгу Tenzornaja Trigonometrija - teorija i prilozenija. – Ninul A. S. (Moscow, Mir, 2004, 336p). см. по ссылке: https://opac.sub.uni-goettingen.de/DB=1/LNG=DU/SID=f7c30ddc-2/CMD?ACT=SRCHA&IKT=1016&SRT=YOP&TRM=tenzornaja+trigonometrija+teorija+i+prilozenija&MATCFILTER=N&MATCSET=N&NOSCAN=N&ADI_BIB= На Google books имеется обновлённое английское издание этой книги (2021г), ISBN 978-5-94052-278-2: https://books.google.ru/books/about?id=0mceEAAAQBAJ The main aims of the given monograph are to develop for beginning a number of geometric notions of the theory of exact matrices and then to work out the basic statements of a tensor trigonometry for bivalent tensor angles formed by linear subspaces or in accordance with their rotation. In the first part (Chapters 1–4) a number of problems from a theory of exact matrices are considered. The general inequality for all average values (means) is formulated; with its use hierarchical invariants for the spectrally positive matrix are installed. Eigen projectors and quasiinverse matrices are expressed in explicit forms – in terms of coefficients of the characteristic polynomial. A minimal annulling polynomial is identified explicitly. The parameters of matrices singularity and inequalities, connected with them, are studied. Null-prime and null-normal singular matrices are defined and considered. In the second part (Chapters 5–12) a tensor trigonometry in affine and metric forms is developed. Binary tensor angles and modulus characteristics for linear objects are determined. The quasi-Euclidean and pseudo-Euclidean tensor trigonometries are constructed in three kinds: projective, reflective and motive (the last term means rotation or deformation). The complete trigonometric spectrum of a null-prime matrix is established, which serves as a basis for obtaining general sine and cosine normalizing inequalities. The quadratic norms of matrices are determined. In Appendix the tensor trigonometry in elementary forms is used for studying motions in non-Euclidean geometries and in a theory of relativity. For summing two- and multistep motions (physical velocities), the polar representation of trigonometric motions (rotations) is used. The law of summing motions (velocities) is given in the general matrix form. The hyperbolic formalizations of Einstein dilation of time and Lorentz contraction of extent are realized mathematically as effects of rotational and deformational transformations of coordinates. The formulae of computation and trigonometric interpretation of secondary orthospherical rotations are given. Trigonometric models for relativistic kinematics and dynamics of a material point in Minkowskian space-time are proposed. Four absolute vector and scalar differentially-geometric and physical characteristics of the curved world line, completely defining its configuration and conformation in the vicinity of every own world point, are considered as the 4D tensor trigonometric pseudoanalog of the 3D classic theory by Frenet–Serret in the Euclidean space. In paper forms this book, without having it, can be looked through in large scientific libraries – Russian and foreign: for instance, in EU – in the most prestigious Zentral Universitätsbibliothek Göttingen as the monograph: Tenzornaja Trigonometrija - teorija i prilozenija. – by Ninul A. S. (Moscow, Mir, 2004, 336p) with the link: https://opac.sub.uni-goettingen.de/DB=1/LNG=DU/SID=f7c30ddc-2/CMD?ACT=SRCHA&IKT=1016&SRT=YOP&TRM=tenzornaja+trigonometrija+teorija+i+prilozenija&MATCFILTER=N&MATCSET=N&NOSCAN=N&ADI_BIB= On the Google books there is an updated English edition of this book (2021), ISBN 978-5-94052-278-2: https://books.google.ru/books/about?id=0mceEAAAQBAJ