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Stochastic processes --- Mathematical potential theory --- 517.9 --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis

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This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.

Measure theory. Mathematical integration --- Integral equations. --- Equations, Integral --- Functional equations --- Functional analysis --- Integral equations --- #TCPW W7.0 --- 517.96 --- 517.96 Finite differences. Functional and integral equations --- Finite differences. Functional and integral equations

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This text presents numerical differential equations to graduate (doctoral) students. It includes the three standard approaches to numerical PDE, FDM, FEM and CM, and the two most common time stepping techniques, FDM and Runge-Kutta. We present both the numerical technique and the supporting theory.The applied techniques include those that arise in the present literature. The supporting mathematical theory includes the general convergence theory. This material should be readily accessible to students with basic knowledge of mathematical analysis, Lebesgue measure and the basics of Hilbert spaces and Banach spaces. Nevertheless, we have made the book free standing in most respects. Most importantly, the terminology is introduced, explained and developed as needed.The examples presented are taken from multiple vital application areas including finance, aerospace, mathematical biology and fluid mechanics. The text may be used as the basis for several distinct lecture courses or as a reference. For instance, this text will support a general applications course or an FEM course with theory and applications. The presentation of material is empirically-based as more and more is demanded of the reader as we progress through the material. By the end of the text, the level of detail is reminiscent of journal articles. Indeed, it is our intention that this material be used to launch a research career in numerical PDE. [Publisher]

Differential equations --- Finite differences --- Finite element method --- Équations différentielles --- Différences finies. --- Éléments finis, Méthode des. --- Numerical solutions --- Solutions numériques.

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Mathematical analysis --- Difference equations --- Social sciences --- Equations aux différences --- Sciences sociales --- Mathematical models --- Modèles mathématiques --- differentiaalvergelijkingen --- 517.9 --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Difference equations. --- Mathematical models. --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Equations aux différences --- Modèles mathématiques

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Functional analysis --- 517.98 --- 517.9 --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory --- Functional analysis.