Advanced Mathematics for Engineers and Physicists
暫譯: 工程師與物理學家的高等數學

Popescu, Sever Angel, Jianu, Marilena

Advanced Mathematics for Engineers and Physicists
  • 出版商: Springer
  • 出版日期: 2023-01-26
  • 售價: $4,180
  • 貴賓價: 9.5 折 $3,971
  • 語言: 英文
  • 頁數: 827
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 303121501X
  • ISBN-13: 9783031215018

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商品描述

This book is designed to be an introductory course to some basic chapters of Advanced Mathematics for Engineering and Physics students, researchers in different branches of Applied Mathematics and anyone wanting to improve their mathematical knowledge by a clear, live, self-contained and motivated text.
Here, one can find different topics, such as differential (first order or higher order) equations, systems of differential equations, Fourier series, Fourier and Laplace transforms, partial differential equations, some basic facts and applications of the calculus of variations and, last but not least, an original and more intuitive introduction to probability theory. All these topics are carefully introduced, with complete proofs, motivations, examples, applications, problems and exercises, which are completely solved at the end of the book.

We added a generous supplementary material (11.1) with a self-contained and complete introduction to normed, metric and Hilbert spaces. Since we used some topics from complex function theory, we also introduced in Chapter 11 a section (11.2) with the basic facts in this important field.

What a reader needs for a complete understanding of this book? For a deep understanding of this book, it is required to take a course in undergraduate calculus and linear algebra. We mostly tried to use the engineering intuition instead of insisting on mathematical tricks. The main feature of the material presented here is its clarity, motivation and the genuine desire of the authors to make extremely transparent the "mysterious" mathematical tools that are used to describe and organize the great variety of impressions that come to the searching mind, from the infinite complexity of Nature.

The book is recommended not only to engineering and physics students or researchers but also to junior students in mathematics because it shows the connection between pure mathematics and physical phenomena, which always supply motivations for mathematical discoveries.

商品描述(中文翻譯)

本書旨在為工程與物理學學生、高級數學的不同應用領域研究者，以及任何希望通過清晰、生動、自足且有動機的文本來提升數學知識的人提供入門課程。
在這裡，讀者可以找到不同的主題，例如微分方程（包括一階或高階微分方程）、微分方程系統、傅立葉級數、傅立葉變換和拉普拉斯變換、偏微分方程、變分法的一些基本事實及應用，最後但同樣重要的是，對概率論的原創且更直觀的介紹。所有這些主題都經過精心介紹，包含完整的證明、動機、範例、應用、問題和練習，這些練習在書末都有完整解答。

我們添加了一個慷慨的補充材料（11.1），提供了對範數空間、度量空間和希爾伯特空間的自足且完整的介紹。由於我們使用了一些複變函數理論的主題，因此在第11章中也介紹了一個部分（11.2），涵蓋這一重要領域的基本事實。

讀者需要什麼才能完全理解本書？要深入理解本書，需修習本科的微積分和線性代數課程。我們主要嘗試使用工程直覺，而不是堅持數學技巧。本書所呈現材料的主要特點是其清晰性、動機以及作者真誠希望使用來描述和組織來自自然無限複雜性的各種印象的「神秘」數學工具變得極為透明的願望。

本書不僅推薦給工程和物理學的學生或研究者，也推薦給數學的初級學生，因為它展示了純數學與物理現象之間的聯繫，這總是為數學發現提供動機。

作者簡介

Sever Angel Popescu. His scientific activity splits into two directions. One is Pure Mathematics, namely, in Algebra and Number theory, where he succeeded in obtaining some interesting results published by known mathematical journals such as Journal of Algebra, Mathematishe Zeitschrift, Mathematiche Nachrihten, Proc. of the Japan Academy, Manuscripta Mathematica, and Acta Arithmetica. (see Google Scholars for instance). The other is in Applied Mathematics, connected to his whole teaching activity at the Technical University of Civil Engineering Bucharest. Here, he tried to apply his mathematical experience to improve the syllabus of advanced mathematics for engineering students. This book covers all his experience in this direction. It is the last book in a series of many other books published in Romanian or in English as courses for engineering students (in Linear Algebra, Mathematical Analysis, Differential Equations, Calculus of Variations, Statistics, etc.). He also published some papers on applied mathematics topics such as differential equations, shift operators, the bridge and torch problem, etc.

Marilena Jianu received her M.Sc. degree in mathematics (statistics and probability) from the University of Bucharest, and her Ph.D. degree in civil engineering from the Technical University of Civil Engineering Bucharest. She has been teaching advanced mathematics to engineering students for over 20 years and has published several papers in pure and applied mathematics. She is an editorial board member of the Romanian Journal of Mathematics and Computer Science and a reviewer for Mathematical Reviews.

作者簡介(中文翻譯)

塞維爾·安傑爾·波佩斯庫。他的科學活動分為兩個方向。一個是純數學，特別是在代數和數論方面，他在這些領域取得了一些有趣的成果，並發表在知名的數學期刊上，如《代數期刊》（Journal of Algebra）、《數學雜誌》（Mathematishe Zeitschrift）、《數學通訊》（Mathematische Nachrichten）、《日本學院會議錄》（Proc. of the Japan Academy）、《數學手稿》（Manuscripta Mathematica）和《算術學報》（Acta Arithmetica）等。（例如，請參見 Google Scholar）。另一個方向是應用數學，與他在布加勒斯特土木工程技術大學的整個教學活動有關。在這裡，他試圖將自己的數學經驗應用於改善工程學生的高等數學課程大綱。本書涵蓋了他在這方面的所有經驗。這是他在羅馬尼亞語或英語中發表的多本書籍系列中的最後一本，這些書籍是為工程學生設計的課程（包括線性代數、數學分析、微分方程、變分法、統計等）。他還發表了一些有關應用數學主題的論文，如微分方程、位移算子、橋樑和火炬問題等。

瑪莉蓮娜·吉安努在布加勒斯特大學獲得數學（統計和概率）碩士學位，並在布加勒斯特土木工程技術大學獲得土木工程博士學位。她已經教授工程學生高等數學超過20年，並在純數學和應用數學領域發表了多篇論文。她是《羅馬尼亞數學與計算機科學期刊》（Romanian Journal of Mathematics and Computer Science）的編輯委員會成員，並擔任《數學評論》（Mathematical Reviews）的審稿人。

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