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Les scalaires et les vecteurs ne peuvent pas représenter toutes les grandeurs physiques ; c'est pourquoi de nouvelles entités mathématiques ont été développées : les tenseurs. Le calcul tensoriel, qui manipule ces grandeurs, est employé, entre autres, en mécanique, en théorie des déformations, en relativité restreinte et générale, ainsi qu'en électromagnétisme. Dans la première partie de l'ouvrage, les tenseurs sont construits et leurs propriétés sont présentées en toute généralité. La deuxième partie est consacrée aux systèmes de coordonnées curvilignes dans l'espace de la géométrie ordinaire et aux procédures d'intégration dans ces systèmes de coordonnées. De plus, la technique du calcul matriciel est développée car elle facilite les manipulations des tableaux de nombres représentant les tenseurs. De nombreux exercices d'application sont proposés avec leurs solutions.

Calculus of tensors. --- Calcul tensoriel.

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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

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Laplace transformation. --- Transformation, Laplace --- Calculus, Operational --- Differential equations --- Transformations (Mathematics)

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"Based on notes written during the teacher's many years of teaching, Analysis in Euclidean Space mainly covers Differentiation and Integration theory in several real variables, but also an array of closely related areas including measure theory, differential geometry, classical theory of curves geometric measure theory, integral geometry, and others. With several original results, new approaches and an emphasis on concepts and rigorous proofs, the book is suitable for undergraduate students, particularly in mathematics and physics, who are interested in acquiring a solid grounding in analysis and expanding their background. There are many examples and exercises inserted in the text for the student to work independently. Analysis in Euclidian Space comprises twenty chapters, each with an introduction summarizing its contents, and an additional chapter containing miscellaneous exercises. Teachers may use the varied chapters of this book for different undergraduate courses in analysis. The only prerequisites are a basic course in linear algebra and a standard first-year calculus course in differentiation and integration. As the book progresses, the difficulty increases such that some of the later sections may be appropriate for graduate study"--

Mathematical analysis. --- Calculus. --- Analyse mathématique. --- Calcul infinitésimal.

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Differential equations.. --- Functional analysis.. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- 517.91 Differential equations --- Differential equations