Problems and Solutions on Vector Spaces for Physicists: From Part I in Mathematical Physics--A Modern Introduction to Its Foundations

Scott, Robert B.

  • 出版商: Springer
  • 出版日期: 2024-08-11
  • 售價: $2,150
  • 貴賓價: 9.5$2,043
  • 語言: 英文
  • 頁數: 178
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031312201
  • ISBN-13: 9783031312205
  • 相關分類: 物理學 Physics
  • 海外代購書籍(需單獨結帳)

相關主題

商品描述

This book offers supporting material for the comprehensive textbook Mathematical Physics--A Modern Introduction to Its Foundations authored by Sadri Hassani. The book covers mathematical preliminaries and all of Part I in Hassani's textbook. The subjects covered here include the key topics necessary for physicists to form a solid mathematical foundation: vectors and linear maps, algebras, operators, matrices, and spectral decomposition. In particular, the vector space concept is a central unifying theme in later chapters of Hassani's textbook. Detailed solutions are provided to one third of the end-of-chapter exercises in the first six chapters of his text.

The present volume helps upper-undergraduate and early postgraduate physics students deepen their understanding of the mathematics that they encounter in physics, learn physics more efficiently, and use mathematics with more confidence and creativity. The content is thus presented rigorously but remains accessible tophysics students.

New exercises are also proposed, some with solutions, some without, so that the total number of unsolved exercises remains unchanged. They are chosen to help explain difficult concepts, amplify key points in Hassani's textbook, or make further connections with applications in physics. Taken together with Hassani's work, the two form a self-contained set and the solutions make detailed reference to Hassani's text. The solutions also refer to other mathematics and physics textbooks, providing entry points to further literature that finds a useful place in the physicist's personal library.

商品描述(中文翻譯)

本書提供了 Sadri Hassani 所著的綜合教科書《數學物理:現代基礎入門》的輔助材料。書中涵蓋了數學基礎知識以及 Hassani 教科書第一部分的所有內容。這裡所涉及的主題包括物理學家建立堅實數學基礎所需的關鍵主題:向量與線性映射、代數、算子、矩陣及譜分解。特別是,向量空間的概念在 Hassani 教科書的後續章節中是一個核心的統一主題。對於他文本前六章的三分之一章末練習題提供了詳細解答。

本書幫助高年級本科生和早期研究生物理學生加深對他們在物理中遇到的數學的理解,更有效地學習物理,並以更大的信心和創造力使用數學。因此,內容雖然嚴謹,但仍然對物理學生可及。

本書還提出了新的練習題,其中一些有解答,有些則沒有,這樣未解的練習題總數保持不變。這些練習題的選擇旨在幫助解釋困難的概念、強調 Hassani 教科書中的關鍵點,或與物理應用建立進一步的聯繫。與 Hassani 的作品結合起來,這兩者形成了一個自足的集合,解答也詳細參考了 Hassani 的文本。解答還提及其他數學和物理教科書,為進一步文獻提供了切入點,這些文獻在物理學家的個人圖書館中佔有一席之地。

作者簡介

Robert B. Scott is a member of the Department of Physics and the Laboratory of Mathematics at the Université de Bretagne Occidentale in Brest, France. He has taught a variety of physics and mathematics courses including:

  • astrophysics and cosmology for physics students
  • quantum mechanics and fundamental physics for mathematicians
  • mathematics for scientists fluid mechanics for engineers, and
  • history of science for humanities students.
While visiting Queen's University in Kingston, Canada, he taught third-year classical mechanics. He is also the author of a similar supporting textbook on general relativity. He has published many research articles on ocean physics and climate dynamics, some pedagogical articles on relativity, and most recently works on biophysics and biological ageing.

作者簡介(中文翻譯)

羅伯特·B·斯科特是法國布雷斯特的西布列塔尼大學物理系及數學實驗室的成員。他教授過多種物理和數學課程,包括:
- 為物理學生開設的天體物理學和宇宙學
- 為數學家開設的量子力學和基礎物理
- 為科學家開設的數學、為工程師開設的流體力學,以及
- 為人文學科學生開設的科學史。

在加拿大金斯頓的女王大學訪問期間,他教授了三年級的經典力學。他還是一本關於廣義相對論的類似輔助教材的作者。他發表了許多有關海洋物理和氣候動力學的研究文章,以及一些關於相對論的教學文章,最近則專注於生物物理學和生物老化的研究。