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Vector analysis. --- Algebra, Universal --- Mathematics --- Numbers, Complex --- Quaternions --- Spinor analysis --- Vector algebra

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Quaternions. --- Numbers, Complex. --- Complex numbers --- Imaginary quantities --- Quantities, Imaginary --- Algebra, Universal --- Quaternions --- Vector analysis --- Algebraic fields --- Curves --- Surfaces --- Numbers, Complex

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Gravitation. --- Calculus of tensors. --- Geometry, Differential. --- Special relativity (Physics) --- General relativity (Physics) --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Physics --- Relativity (Physics) --- Ether drift --- Mass energy relations --- Relativity theory, Special --- Restricted theory of relativity --- Special theory of relativity --- Differential geometry --- Absolute differential calculus --- Analysis, Tensor --- Calculus, Absolute differential --- Calculus, Tensor --- Tensor analysis --- Tensor calculus --- Geometry, Differential --- Geometry, Infinitesimal --- Vector analysis --- Spinor analysis --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Properties

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This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. In addition, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.

Mathematics. --- Functional analysis. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Measure theory. --- Probabilities. --- Functional Analysis. --- Global Analysis and Analysis on Manifolds. --- Measure and Integration. --- Probability Theory and Stochastic Processes. --- Vector spaces. --- Linear spaces --- Linear vector spaces --- Algebras, Linear --- Functional analysis --- Vector analysis --- Global analysis. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Math --- Science --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic

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This book presents the fundamentals of modern tensor calculus for students in engineering and applied physics, emphasizing those aspects that are crucial for applying tensor calculus safely in Euclidian space and for grasping the very essence of the smooth manifold concept. After introducing the subject, it provides a brief exposition on point set topology to familiarize readers with the subject, especially with those topics required in later chapters. It then describes the finite dimensional real vector space and its dual, focusing on the usefulness of the latter for encoding duality concepts in physics. Moreover, it introduces tensors as objects that encode linear mappings and discusses affine and Euclidean spaces. Tensor analysis is explored first in Euclidean space, starting from a generalization of the concept of differentiability and proceeding towards concepts such as directional derivative, covariant derivative and integration based on differential forms. The final chapter addresses the role of smooth manifolds in modeling spaces other than Euclidean space, particularly the concepts of smooth atlas and tangent space, which are crucial to understanding the topic. Two of the most important concepts, namely the tangent bundle and the Lie derivative, are subsequently worked out.

Calculus of tensors. --- Manifolds (Mathematics) --- Absolute differential calculus --- Analysis, Tensor --- Calculus, Absolute differential --- Calculus, Tensor --- Tensor analysis --- Tensor calculus --- Engineering. --- Mathematical physics. --- Physics. --- Continuum mechanics. --- Continuum Mechanics and Mechanics of Materials. --- Classical and Continuum Physics. --- Mathematical Applications in the Physical Sciences. --- Mathematical Methods in Physics. --- Geometry, Differential --- Topology --- Geometry, Infinitesimal --- Vector analysis --- Spinor analysis --- Mechanics. --- Mechanics, Applied. --- Solid Mechanics. --- Physical mathematics --- Physics --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Mathematics --- Continuum physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Classical field theory --- Continuum physics --- Continuum mechanics