A Short Introduction to Partial Differential Equations

Novruzi, Arian

A Short Introduction to Partial Differential Equations
  • 出版商: Springer
  • 出版日期: 2023-12-31
  • 售價: $3,070
  • 貴賓價: 9.5 折 $2,917
  • 語言: 英文
  • 頁數: 219
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031395239
  • ISBN-13: 9783031395239

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商品描述

This book provides a short introduction to partial differential equations (PDEs). It is primarily addressed to graduate students and researchers, who are new to PDEs. The book offers a user-friendly approach to the analysis of PDEs, by combining elementary techniques and fundamental modern methods.

The author focuses the analysis on four prototypes of PDEs, and presents two approaches for each of them. The first approach consists of the method of analytical and classical solutions, and the second approach consists of the method of weak (variational) solutions.

In connection with the approach of weak solutions, the book also provides an introduction to distributions, Fourier transform and Sobolev spaces. The book ends with an appendix chapter, which complements the previous chapters with proofs, examples and remarks.

This book can be used for an intense one-semester, or normal two-semester, PDE course. The reader isexpected to have knowledge of linear algebra and of differential equations, a good background in real and complex calculus and a modest background in analysis and topology. The book has many examples, which help to better understand the concepts, highlight the key ideas and emphasize the sharpness of results, as well as a section of problems at the end of each chapter.

商品描述(中文翻譯)

這本書提供了對偏微分方程（PDEs）的簡要介紹。主要針對研究生和新手研究者。本書結合基礎技巧和現代基本方法，以用戶友好的方式進行PDEs分析。

作者將分析重點放在四種PDEs的原型上，並為每種原型提供兩種方法。第一種方法是解析和經典解的方法，第二種方法是弱（變分）解的方法。

關於弱解的方法，本書還介紹了分布、傅立葉變換和Sobolev空間。書末附有一個附錄章節，補充了前面章節的證明、例子和備註。

這本書可以用於一個密集的一學期或正常的兩學期PDE課程。讀者需要具備線性代數和微分方程的知識，以及良好的實數和複數微積分背景，以及分析和拓撲的基礎知識。本書有許多例子，有助於更好地理解概念，突出關鍵思想，強調結果的嚴謹性，每章末尾還有一個問題部分。

作者簡介

The author is a professor of Mathematics at University of Ottawa, Canada (since 2002). He holds a PhD in Mathematics from University Henri Poincare, Nancy, France, 1997. Before joining University of Ottawa in 2002, he had held postdoctoral positions at INRIA France and PIMS, UBC, Vancouver, Canada. The author's main research area are Shape Optimization and Partial Differential Equations, as they are integral part of his research. The author has taught PDEs at University of Ottawa for many years, and this book represents this teaching experience.

作者簡介(中文翻譯)

作者是加拿大渥太華大學的數學教授（自2002年起）。他在1997年獲得法國南希亨利·庞加莱大學的數學博士學位。在2002年加入渥太華大學之前，他曾在法國INRIA和加拿大溫哥華UBC的PIMS擔任博士後職位。作者的主要研究領域是形狀優化和偏微分方程，它們是他研究的重要組成部分。作者多年來在渥太華大學教授偏微分方程，本書代表了他的教學經驗。

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