Partial Differential Equations in Action: From Modelling to Theory 4th ed. 2022 Edition

Salsa, Sandro, Verzini, Gianmaria

Partial Differential Equations in Action: From Modelling to Theory 4th ed. 2022 Edition
  • 出版商: Springer
  • 出版日期: 2022-12-09
  • 售價: $3,150
  • 貴賓價: 9.5 折 $2,993
  • 語言: 英文
  • 頁數: 677
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031218523
  • ISBN-13: 9783031218521

    • 立即出貨(限量) (庫存=2)

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商品描述

This work is an updated version of a book evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In the second part, chapters 6 to 10 concentrate on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems, while Chapter 11 deals with vector-valued conservation laws, extending the theory developed in Chapter 4. The main differences with respect to the previous editions are: a new section on reaction diffusion models for population dynamics in a heterogeneous environment; several new exercises in almost all chapters; a general restyling and a reordering of the last chapters. The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering.

 

 

 

商品描述(中文翻譯)

這本書是從最近幾年在米蘭理工大學開設的偏微分方程（PDE）課程中演變而來的更新版本。這些課程有兩個目的：一方面是教導學生欣賞應用科學中出現的理論和建模之間的相互作用，另一方面是為他們提供堅實的理論基礎，以應用於數值方法，如有限元素。因此，這本教科書分為兩個部分。第一部分，第2章到第5章，性質較為基礎，重點是發展和研究來自擴散、傳播和運輸、波動和振動等宏觀領域的基本問題。在第二部分，第6章到第10章集中於發展希爾伯特空間方法，用於變分形式和（主要是）線性邊界和初邊值問題的分析，而第11章則處理向量值守恆定律，擴展了第4章中發展的理論。與以前版本相比，主要的差異包括：在異質環境中的人口動態反應擴散模型的新節；幾乎所有章節中的多個新練習題；整體風格的改進和最後幾章的重新排序。本書旨在為來自不同學科（包括應用數學、物理和工程學）的高年級本科生或研究生提供高級課程。

作者簡介

Sandro Salsa is a Emeritus Professor of Mathematical Analysis at Politecnico of Milan, where he has been one of the main founders of the educational program in Mathematical Engineering. His research interest ranges over diverse aspects of nonlinear, nonlocal, singular or degenerate elliptic and parabolic equations, with particular emphasis on boundary behavior, regularity and free boundary problems. He is an author of 14 books and several papers in the most prestigious scientific mathematical journals.

Gianmaria Verzini is a Professor of Mathematical Analysis at the Department of Mathematics of the Politecnico of Milan. He is author of 5 books and more than 50 papers, published on prominent international journals. His scientific interests concern the applications of Nonlinear Analysis to the existence, multiplicity, qualitative properties and regularity of solutions to nonlinear differential equations and systems.

作者簡介(中文翻譯)

Sandro Salsa是米蘭理工大學的數學分析名譽教授，他是數學工程教育計劃的主要創始人之一。他的研究興趣涵蓋非線性、非局部、奇異或退化橢圓和抛物型方程的各個方面，尤其關注邊界行為、正則性和自由邊界問題。他是14本書籍和多篇發表在最負盛名的科學數學期刊上的論文的作者。

Gianmaria Verzini是米蘭理工大學數學系的數學分析教授。他是5本書籍和50多篇發表在知名國際期刊上的論文的作者。他的科學興趣涉及非線性分析在非線性微分方程和系統的解的存在性、多樣性、質量特性和正則性方面的應用。

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