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Titlebook: Essential Partial Differential Equations; Analytical and Compu David F. Griffiths,John W. Dold,David J. Silvester Textbook 2015 Springer Na

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書(shū)目名稱Essential Partial Differential Equations
副標(biāo)題Analytical and Compu
編輯David F. Griffiths,John W. Dold,David J. Silvester
視頻videohttp://file.papertrans.cn/316/315502/315502.mp4
概述Analytical and computational approach to PDEs.Contains 300 exercises, all with full solutions, starred according to difficulty.One chapter dedicated to projects intended for individual or group study.
叢書(shū)名稱Springer Undergraduate Mathematics Series
圖書(shū)封面Titlebook: Essential Partial Differential Equations; Analytical and Compu David F. Griffiths,John W. Dold,David J. Silvester Textbook 2015 Springer Na
描述.This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems..The underlying theory is illustrated by numerous examples and there are around 300 exercises, designedto promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised
出版日期Textbook 2015
關(guān)鍵詞Discrete Fourier Analysis; Energy Methods; Finite Difference Approximation; Maximum Principles; Method o
版次1
doihttps://doi.org/10.1007/978-3-319-22569-2
isbn_softcover978-3-319-22568-5
isbn_ebook978-3-319-22569-2Series ISSN 1615-2085 Series E-ISSN 2197-4144
issn_series 1615-2085
copyrightSpringer Nature Switzerland AG 2015
The information of publication is updating

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Argument as Conflict: Then and Now,This chapter introduces the notion of a partial differential equation. Some fundamentally important PDEs are identified and some classical solutions are discussed. The chapter motivates the analytical and numerical solution techniques that are developed in the remainder of the book.
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Conflict and Multimodal CommunicationThis chapter focuses on one-dimensional boundary value problems. Key concepts like maximum principles, comparison principles and infinite series solutions are introduced in a one-dimensional setting. This chapter establishes the theoretical framework that is used to establish the well-posedness of PDE problems in later chapters.
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Hamoon Khelghat-Doost,Deniz ülke Ar?bo?anThis chapter extends the ideas in earlier chapters and identifies two concepts that are useful for checking the well-posedness of boundary value problems. These concepts play a fundamental role in establishing the stability of finite difference solutions in later chapters.
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Conflict in Northeast India: An Overview,This chapter describes a classical technique for constructing solutions of hyperbolic PDEs. The method is applied to linear systems of PDEs and to nonlinear PDE problems. This naturally leads to a discussion of more advanced topics including shocks, Riemann problems and weak solutions.
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Setting the Scene,This chapter introduces the notion of a partial differential equation. Some fundamentally important PDEs are identified and some classical solutions are discussed. The chapter motivates the analytical and numerical solution techniques that are developed in the remainder of the book.
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發(fā)表于 2025-3-23 08:24:06 | 只看該作者
Boundary Value Problems in , ,This chapter focuses on one-dimensional boundary value problems. Key concepts like maximum principles, comparison principles and infinite series solutions are introduced in a one-dimensional setting. This chapter establishes the theoretical framework that is used to establish the well-posedness of PDE problems in later chapters.
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