环境科学家和工程师的数值偏微分方程：第一门实践课程

English | PDF | 2005 | 390 Pages | ISBN : 0387236198 | 15.9 MB

This book concerns the practical solution of Partial Differential Equations. We assume the reader knows what a PDE is - that he or she has derived some, and solved them with the limited but powerful arsenal of analytic techniques. We also assume that (s)he has gained some intuitive knowledge of their solution properties, either in the context of specific applications, or in the more abstract context of applied mathematics. We assume the reader now wants to solve PDE's for real, in the context of practical problems with all of their warts - awkward geometry, driven by real data, variable coefficients, nonlinearities - as they arise in real situations. The applications we envision span classical mathematical physics and the "engineering sciences" : fluid mechanics, solid mechanics, electricity and magnetism, heat and mass transfer, wave propagation. Of course, these all share a joyous interdisciplinary unity in PDE's. The material arises from lectures at Dartmouth College for first-year graduate students in science and engineering. That audience has shared the above motivations, and a mathematical background including: ordinary and partial differential equations; a first course in numerical an- ysis; linear algebra; complex numbers at least at the level of Fourier analysis; and an ability to program modern computers. Some working exposure to applications of PDE's in their research or practice has also been a common denominator. This classical undergraduate preparation sets the stage for our "First Practical Course". Naturally, the "practical" aspect of the course involves computation.

中文|PDF|2005|390页|ISBN:0387236198|15.9 MB这本书涉及偏微分方程的实际解。我们假设读者知道PDE是什么——他或她已经推导出了一些PDE，并用有限但强大的分析技术库解决了它们。我们还假设，无论是在特定应用的背景下，还是在更抽象的应用数学背景下，他都对它们的解的性质有了一些直观的了解。我们假设读者现在想在实际问题的背景下真实地解决偏微分方程，因为它们在真实情况下出现了所有缺点——由真实数据驱动的尴尬几何、可变系数、非线性。我们设想的应用涵盖了经典数学物理和“工程科学”：流体力学、固体力学、电学和磁学、传热传质、波传播。当然，这些都在偏微分方程中有着欢乐的跨学科统一。这些材料来自达特茅斯学院为科学和工程专业一年级研究生举办的讲座。这些听众分享了上述动机和数学背景，包括：常微分方程和偏微分方程；数值分析的第一门课程；线性代数；至少在傅里叶分析水平上的复数；以及为现代计算机编程的能力。在他们的研究或实践中，对PDE应用的一些工作接触也是一个共同点。这种经典的本科准备为我们的“第一门实践课程”奠定了基础。当然，该课程的“实践”方面涉及计算。

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