| 书目名称 | Partial Differential Equations | | 副标题 | An Introduction to A | | 编辑 | Wolfgang Arendt,Karsten Urban | | 视频video | | | 概述 | Intertwines analytical and numerical methods for an integrated approach.Showcases examples from the physical sciences, engineering, and economics.Includes numerous exercises, illustrations, and opport | | 丛书名称 | Graduate Texts in Mathematics | | 图书封面 |  | | 描述 | .This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach...A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses onfinite difference and finite element methods. Computer-aided calculation with Maple™ completes the book. Throughout, three fundamental examples are studied with different tools: Poisson’s equation, the heat equ | | 出版日期 | Textbook 2023 | | 关键词 | partial differential equations textbook; partial differential equations modeling; partial differential | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-13379-4 | | isbn_softcover | 978-3-031-13381-7 | | isbn_ebook | 978-3-031-13379-4Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 18:18:54
