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Random matrices. --- Wigner distribution. --- Integrals, Stieltjes. --- Matrices aléatoires. --- Wigner, Distribution de. --- Stieltjes, Intégrales de. --- Functions of complex variables. --- Integral equations. --- Analytic functions. --- Vector algebra --- Algebra, Vector --- Algebras, Linear --- Vector analysis

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Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.

Calculus of tensors. --- Absolute differential calculus --- Analysis, Tensor --- Calculus, Absolute differential --- Calculus, Tensor --- Tensor analysis --- Tensor calculus --- Geometry, Differential --- Geometry, Infinitesimal --- Vector analysis --- Spinor analysis --- Numerical analysis. --- Chemistry, Physical and theoretical. --- Mathematical physics. --- Numerical Analysis. --- Theoretical and Computational Chemistry. --- Theoretical, Mathematical and Computational Physics. --- Physical mathematics --- Physics --- Chemistry, Theoretical --- Physical chemistry --- Theoretical chemistry --- Chemistry --- Mathematical analysis --- Mathematics

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This textbook develops Special Relativity in a systematic way and offers the unique feature of having more than 200 problems with detailed solutions to empower students to gain a real understanding of this core subject in physics. This new edition has been thoroughly updated and has new sections on relativistic fluids, relativistic kinematics and on four-acceleration. The problems and solution section has been significantly expanded and short history sections have been included throughout the book. The approach is structural in the sense that it develops Special Relativity in Minkowski space following the parallel steps as the development of Newtonian Physics in Euclidian space. A second characteristic of the book is that it discusses the mathematics of the theory independently of the physical principles, so that the reader will appreciate their role in the development of the physical theory. The book is intended to be used both as a textbook for an advanced undergraduate teaching course in Special Relativity but also as a reference book for the future.

Special relativity (Physics) --- Calculus of tensors --- Absolute differential calculus --- Analysis, Tensor --- Calculus, Absolute differential --- Calculus, Tensor --- Tensor analysis --- Tensor calculus --- Geometry, Differential --- Geometry, Infinitesimal --- Vector analysis --- Spinor analysis --- Ether drift --- Mass energy relations --- Relativity theory, Special --- Restricted theory of relativity --- Special theory of relativity --- Relativity (Physics) --- Classical and Quantum Gravitation, Relativity Theory. --- Cosmology. --- Mathematical Applications in the Physical Sciences. --- Astronomy --- Deism --- Metaphysics --- Gravitation. --- Mathematical physics. --- Physical mathematics --- Physics --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Mathematics --- Properties --- Relativitat especial (Física) --- Educació superior --- Física matemàtica --- Educació universitària --- Ensenyament superior --- Ensenyament universitari --- Estudis superiors --- Estudis universitaris --- Etapes educatives --- Abandó dels estudis (Educació superior) --- Competències transversals --- Educació clàssica --- Ensenyament de la biblioteconomia --- Estudis de postgrau --- Extensió universitària --- Lectura (Educació superior) --- Orientació en l'educació superior --- Primer cicle d'ensenyament universitari --- Seminaris --- Tercer cicle d'ensenyament universitari --- Campus virtuals --- Escrits acadèmics --- Pràcticums --- Universitats --- Relativitat restringida --- Teoria de la relativitat especial --- Relativitat (Física) --- Teoria quàntica relativista --- Mecànica --- Acústica --- Anàlisi de sistemes --- Anàlisi dimensional --- Grups quàntics --- Elasticitat --- Equació de Yang-Baxter --- Matemàtica en l'electrònica --- Problemes de contorn --- Teoria del potencial (Física) --- Teoria ergòdica --- Teories no lineals --- Rutes aleatòries (Matemàtica) --- Educació superior transfronterera --- Classical and Quantum Gravity. --- Mathematical Physics.