Essays in Linear Algebra
暫譯: 線性代數隨筆

Strang, Gilbert

Essays in Linear Algebra
  • 出版商: Cambridge
  • 出版日期: 2012-04-26
  • 售價: $2,050
  • 貴賓價: 9.5 折 $1,947
  • 語言: 英文
  • 頁數: 340
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 0980232767
  • ISBN-13: 9780980232769
  • 相關分類: 線性代數 Linear-algebra

    • 已絕版

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商品描述

The renowned mathematician and educator Gilbert Strang presents a collection of expository papers on the theory and applications of linear algebra, accompanied by video lectures on http: //ocw.mit.edu. The essays are diverse in scope and range from purely theoretical studies on deep fundamental principles of matrix algebra to discussions on the teaching of calculus and an examination of the mathematical foundations of aspects of computational engineering. One thing these essays have in common is the way that they express both the importance and the beauty of the subject, as well as the author's passion for mathematics. This text will be of practical use to students and researchers across a whole spectrum of numerate disciplines. Furthermore, this collection provides a unique perspective on mathematics and the communication thereof as a human endeavour, complemented as these essays are by commentary from the author regarding their provenance and the reaction to them

商品描述(中文翻譯)

著名的數學家和教育家吉爾伯特·斯特朗（Gilbert Strang）呈現了一系列關於線性代數理論及其應用的說明性論文，並附有在 http://ocw.mit.edu 上的視頻講座。這些論文的範疇多樣，從純理論的矩陣代數基本原則深入研究，到對微積分教學的討論，以及對計算工程某些方面數學基礎的檢視。這些論文共同的特點是表達了該學科的重要性和美感，以及作者對數學的熱情。這本書對於各種數學相關學科的學生和研究人員都具有實用價值。此外，這個合集提供了對數學及其作為人類努力的溝通的獨特視角，並附有作者對這些論文來源及其反應的評論。

作者簡介

Gilbert Strang, Massachusetts Institute of Technology
Gilbert Strang is a professor of mathematics at the Massachusetts Institute of Technology, where his research focuses on analysis, linear algebra and PDEs. In addition, he is the author of many textbooks and his service to the mathematics community is extensive, having spent time as President of SIAM, Chair of the Joint Policy Board for Mathematics as well as membership of various other committees and boards. The awards that Professor Strang has received for his research and teaching include the Chauvenet Prize (1976), the Award for Distinguished Service (SIAM, 2003), the Graduate School Teaching Award (MIT, 2003) and the Von Neumann Prize Medal of the U.S. Association for Computational Mechanics (2005), among others. He is a Member of the National Academy of Sciences, a Fellow of the American Academy of Arts and Sciences and an Honorary Fellow of Balliol College, Oxford.

作者簡介(中文翻譯)

吉爾伯特·斯特朗，麻省理工學院

吉爾伯特·斯特朗是麻省理工學院的數學教授，他的研究專注於分析、線性代數和偏微分方程（PDEs）。此外，他還是多本教科書的作者，並在數學社群中擔任過多項重要職務，包括美國數學學會（SIAM）會長、數學聯合政策委員會主席，以及其他多個委員會和董事會的成員。斯特朗教授因其研究和教學所獲得的獎項包括喬文內獎（Chauvenet Prize，1976年）、傑出服務獎（SIAM，2003年）、研究生院教學獎（麻省理工學院，2003年）以及美國計算力學協會的馮·諾依曼獎章（2005年）等。他是美國國家科學院的成員、美國藝術與科學學院的院士，以及牛津大學巴利奧學院的榮譽院士。

目錄大綱

Part I. Essays in Linear Algebra:
1. Perfect bases for the four subspaces
2. Four subspaces from a graph
3. My favourite matrix
4. The ultimate in echelon forms
5. Diagonalizing a symmetric matrix
6. Pascal's triangle in three matrices
7. Can the factors be sparse?
8. The eigenvalues of AB + BA
9. Factoring into very special matrices
10. Toeplitz matrices and circulants
11. The joint spectral radius of A and B
12. Banded matrices have remarkable inverses
Part II. Essays in Calculus:
13. The fundamental theorem of calculus
14. The great function of calculus
15. Thin strips and small triangles in calculus
16. Chaos in Newton's method
17. Optical illusions for y = sin n
Part III. Essays in Applied Mathematics:
18. The principles of applied mathematics
19. A minimum equals a maximum
20. Aiming directly at the solution
21. A chair through a door
Part IV. Essays in Computational Science:
22. Eight cosine transforms
23. The ideas behind finite elements
24. The Strang–Fix conditions
25. Wavelets in music and television
26. Scaling functions lead to wavelets
27. Old and new splitting methods
An essay about books
List of publications
Index.

目錄大綱(中文翻譯)

Part I. Essays in Linear Algebra:

1. Perfect bases for the four subspaces

2. Four subspaces from a graph

3. My favourite matrix

4. The ultimate in echelon forms

5. Diagonalizing a symmetric matrix

6. Pascal's triangle in three matrices

7. Can the factors be sparse?

8. The eigenvalues of AB + BA

9. Factoring into very special matrices

10. Toeplitz matrices and circulants

11. The joint spectral radius of A and B

12. Banded matrices have remarkable inverses

Part II. Essays in Calculus:

13. The fundamental theorem of calculus

14. The great function of calculus

15. Thin strips and small triangles in calculus

16. Chaos in Newton's method

17. Optical illusions for y = sin n

Part III. Essays in Applied Mathematics:

18. The principles of applied mathematics

19. A minimum equals a maximum

20. Aiming directly at the solution

21. A chair through a door

Part IV. Essays in Computational Science:

22. Eight cosine transforms

23. The ideas behind finite elements

24. The Strang–Fix conditions

25. Wavelets in music and television

26. Scaling functions lead to wavelets

27. Old and new splitting methods

An essay about books

List of publications

Index.

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