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標(biāo)題: Titlebook: Introduction to Partial Differential Equations; David Borthwick Textbook 2016 Springer Nature Switzerland AG 2016 linear equations.partial [打印本頁]

作者: deep-sleep    時間: 2025-3-21 19:09
書目名稱Introduction to Partial Differential Equations影響因子(影響力)




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Textbook 2016t important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.?.Within each section the author creates a narrative that ans
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https://doi.org/10.1007/978-3-319-48936-0linear equations; partial differential equations; Laplace equation; mathematical analysis; wave equation
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978-3-319-84051-2Springer Nature Switzerland AG 2016
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Introduction,Continuous phenomena, such as wave propagation or fluid flow, are generally modeled with . (PDE), which express relationships between rates of change with respect to multiple independent variables.
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Separation of Variables,Some PDE can be split into pieces that involve distinct variables. For PDE that admit separation, it is natural to look for product solutions whose factors depend on the separate variables.
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The Heat Equation,In this chapter we will discuss the derivation of the heat equation and develop some basic properties, our first example of a PDE of parabolic type.
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Maximum Principles,In this chapter we will consider another approach to issues of uniqueness and stability, based on maximum values. This method applies generally to elliptic equations, which describe equilibrium states, and to parabolic equations, which are generally used to model diffusion.
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Weak Solutions,As noted in Sect.?., it is possible to define weak solutions of a PDE that are not sufficiently differentiable to solve the equation literally. In this chapter we will discuss the mathematical formulation of this generalized notion of solution.
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Variational Methods,In this chapter we will develop a strategy that involves reformulating a PDE in terms of a minimization problem on a function space.
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Distributions,To define weak derivatives in Chap.?., we measured the values of a solution using test functions. Taking this idea one step further leads to a generalization of the concept of a function, called a distribution.
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David BorthwickPerfect book for a ?One-semester PDE course.Includes a thorough discussion of modeling process for each equation.Covers indepth three types of linear PDES: elliptic, parabolic, and hyperbolic?.Include
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David Borthwicked, that provide rehabilitation, treatment, and treatment planning services. This encyclopedia will serve as a unified, comprehensive reference for professionals involved in the diagnosis, evaluation, and rehab978-0-387-79948-3
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0172-5939 did we obtain by developing and analyzing the PDE?.The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspirationfor the development of methods.?.978-3-319-84051-2978-3-319-48936-0Series ISSN 0172-5939 Series E-ISSN 2191-6675
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