A Compact Course on Linear Pdes
暫譯: 線性偏微分方程的精簡課程
Valli, Alberto
- 出版商: Springer
- 出版日期: 2023-08-30
- 售價: $2,440
- 貴賓價: 9.5 折 $2,318
- 語言: 英文
- 頁數: 262
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031359755
- ISBN-13: 9783031359750
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相關主題
商品描述
This textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces. It contains elliptic equations, including the biharmonic problem, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, some basic results on Fredholm alternative and spectral theory, saddle point problems, parabolic and linear Navier-Stokes equations, and hyperbolic and Maxwell equations. Almost 80 exercises are added, and the complete solution of all of them is included. The work is mainly addressed to students in Mathematics, but also students in Engineering with a good mathematical background should be able to follow the theory presented here. This second edition has been enriched by some new sections and new exercises; in particular, three important equations are now included: the biharmonic equation, the linear Navier-Stokes equations and the Maxwell equations.
商品描述(中文翻譯)
這本教科書專注於二階線性偏微分方程。重點在於希爾伯特空間中的變分形式。內容包括橢圓方程，涵蓋雙調和問題、一些有用的泛函分析筆記、Sobolev 空間及其性質的簡要介紹、Fredholm 替代定理和譜理論的一些基本結果、鞍點問題、拋物線和線性 Navier-Stokes 方程，以及雙曲線和 Maxwell 方程。書中附有近80道習題，並包含所有習題的完整解答。本書主要針對數學專業的學生，但具備良好數學基礎的工程學生也應能理解這裡所呈現的理論。本第二版增添了一些新章節和新習題；特別是，現在包含了三個重要方程：雙調和方程、線性 Navier-Stokes 方程和 Maxwell 方程。
作者簡介
Alberto Valli is a Professor of Mathematical Analysis at University of Trento. His research activity has focused on the mathematical analysis of linear and nonlinear partial differential equations, in particular in fluid dynamics and electromagnetism, and on their numerical approximation by means of the finite element method. He published more than 80 papers in prestigious international journals and 4 books on partial differential equations and their numerical approximation.
作者簡介(中文翻譯)
阿爾貝托·瓦利是特倫托大學的數學分析教授。他的研究活動專注於線性和非線性偏微分方程的數學分析，特別是在流體力學和電磁學方面，以及通過有限元素法對這些方程的數值近似。他在國際知名期刊上發表了超過80篇論文，並出版了4本關於偏微分方程及其數值近似的書籍。
