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Linear Algebra: Algorithms, Applications, and Techniques, Fourth Edition offers a modern and algorithmic approach to computation while providing clear and straightforward theoretical background information. The book guides readers through the major applications, with chapters on properties of real numbers, proof techniques, matrices, vector spaces, linear transformations, eigen values, and Euclidean inner products. Appendices on Jordan canonical forms and Markov chains are included for further study. This useful textbook presents broad and balanced views of theory, with key material highlighted and summarized in each chapter. To further support student practice, the book also includes ample exercises with answers and hints.

Algebras, Linear. --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology

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Covering an exciting and active area of research at the crossroads of several different fields in mathematics and physics, and drawing on the author's previous work, this text has been written to explain the advanced mathematics involved simply and clearly to graduate students in both disciplines.

Geometry, Riemannian. --- Holonomy groups. --- Groups, Holonomy --- Geometry, Differential --- Riemann geometry --- Riemannian geometry --- Generalized spaces --- Geometry, Non-Euclidean --- Semi-Riemannian geometry --- Riemann, Géométrie de

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This textbook offers a comprehensive coverage of the fundamentals of calculus, linear algebra and analytic geometry. Intended for bachelor’s students in science, engineering, architecture, economics, the presentation is self-contained, and supported by numerous graphs, to facilitate visualization and also to stimulate readers’ intuition. The proofs of the theorems are rigorous, yet presented in straightforward and comprehensive way. With a good balance between algebra, geometry and analysis, this book guides readers to apply the theory to solve differential equations. Many problems and solved exercises are included. Students are expected to gain a solid background and a versatile attitude towards calculus, algebra and geometry, which can be later used to acquire new skills in more advanced scientific disciplines, such as bioinformatics, process engineering, and finance. At the same time, instructors are provided with extensive information and inspiration for the preparation of their own courses.

Engineering mathematics. --- Algebras, Linear. --- Mathematics. --- Engineering Mathematics. --- Linear Algebra. --- Applications of Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Math --- Science --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Calculus of operations --- Line geometry --- Topology --- Mathematics --- Calculus. --- Geometric analysis. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal --- Geometric analysis PDEs (Geometric partial differential equations) --- Geometry --- Càlcul --- Àlgebra lineal

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Setting forth the basic principles of tensors and manifolds, this book describes how the mathematics underlie elegant geometrical models of classical mechanics, relativity and elementary particle physics.

Calculus of tensors. --- Manifolds (Mathematics) --- Mathematical physics. --- Generalized spaces. --- Mechanics. --- Relativity (Physics) --- Gravitation --- Nonrelativistic quantum mechanics --- Space and time --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Geometry of paths --- Minkowski space --- Spaces, Generalized --- Weyl space --- Calculus of tensors --- Geometry, Differential --- Geometry, Non-Euclidean --- Hyperspace --- Physical mathematics --- Topology --- Absolute differential calculus --- Analysis, Tensor --- Calculus, Absolute differential --- Calculus, Tensor --- Tensor analysis --- Tensor calculus --- Geometry, Infinitesimal --- Vector analysis --- Spinor analysis --- Mathematics

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This book comprises select peer-reviewed articles submitted for the proceedings of the International Conference on Mathematics and Computing (ICMC 2022), held by the School of Advanced Sciences, Vellore Institute of Technology, Vellore, India, in association with Ramanujan Mathematical Society, India, Cryptology Research Society of India and Society for Electronic Transactions and Security, India, from 6–8 January 2022. With an aim to identify the existing challenges in the areas of mathematics and computing, the book emphasizes the importance of establishing new methods and algorithms to address these challenges. The book includes topics on diverse applications of cryptology, network security, cyber security, block chain, IoT, mobile network, data analytics, applied algebra, mathematical analysis, mathematical modelling, fluid dynamics, fractional calculus, multi-optimization, integral equations, dynamical systems, numerical analysis and scientific computing. Divided into five major parts—applied algebra and analysis, fractional calculus and integral equations, mathematical modelling and fluid dynamics, numerical analysis, and computer science and applications—the book is a useful resource for students, researchers and faculty as well as practitioners.

Algebras, Linear. --- Mathematical analysis. --- Integral equations. --- Fluid mechanics. --- Numerical analysis. --- Mathematical models. --- Linear Algebra. --- Analysis. --- Integral Equations. --- Engineering Fluid Dynamics. --- Numerical Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Informàtica --- Àlgebra lineal --- Anàlisi matemàtica --- Models matemàtics --- Models, Mathematical --- Simulation methods --- Mathematical analysis --- Hydromechanics --- Continuum mechanics --- Equations, Integral --- Functional equations --- Functional analysis --- 517.1 Mathematical analysis --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Calculus of operations --- Line geometry --- Topology --- Models (Matemàtica) --- Models experimentals --- Models teòrics --- Mètodes de simulació --- Anàlisi de sistemes --- Mètode de Montecarlo --- Modelització multiescala --- Models economètrics --- Models lineals (Estadística) --- Models multinivell (Estadística) --- Models no lineals (Estadística) --- Programació (Ordinadors) --- Simulació per ordinador --- Teoria de màquines --- Models biològics --- Matemàtica --- Anàlisi combinatòria --- Anàlisi de Fourier --- Anàlisi estocàstica --- Anàlisi matemàtica no-estàndard --- Anàlisi numèrica --- Funcions --- Matemàtica per a enginyers --- Sèries infinites --- Teoria del potencial (Matemàtica) --- Teories no lineals --- Rutes aleatòries (Matemàtica) --- Àlgebra --- Càlcul --- Àlgebra universal --- Espais generalitzats --- Àlgebra tensorial --- Àlgebra vectorial --- Àlgebres de Clifford --- Àlgebres de Jordan --- Àlgebres de Lie --- Complexos (Matemàtica) --- Espais vectorials --- Topologia --- Enginyeria --- Càlcul intensiu (Informàtica) --- Disseny de sistemes --- Història de la informàtica --- Geometria computacional --- Informàtica tova --- Processament de dades --- Sistemes informàtics --- Teledocumentació --- Tractament del llenguatge natural (Informàtica) --- Automatització d'arxius --- Automatització de biblioteques --- Automatització de museus --- Indústria informàtica --- Teoria de la informació