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《麻省理工开放课程:线性代数》(Linear Algebra)英文字幕包/共34课更新完毕[MP4]

  • 状态: 精华资源
  • 摘要:
    课程类型数学
    发行日期2005年
    对白语言英语
  • 时间: 2010/08/10 18:06:13 发布 | 2010/08/23 10:45:08 更新
  • 分类: 教育  理工科 

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中文名麻省理工开放课程:线性代数
英文名Linear Algebra
资源格式MP4
课程类型数学
学校麻省理工 MIT
版本英文字幕包/共34课更新完毕
发行日期2005年
地区美国
对白语言英语
简介

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课程介绍:
这个基础课程主要阐述矩阵理论和线性代数。主题 重点放在对在其他学科的有用的法则上面,包括方程组,向量空间,行列式,特征值,相似性,以及正定矩阵。

导师介绍
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Gilbert Strang was an undergraduate at MIT and a Rhodes Scholar at Balliol College, Oxford. His Ph.D. was from UCLA and since then he has taught at MIT. He has been a Sloan Fellow and a Fairchild Scholar and is a Fellow of the American Academy of Arts and Sciences. He is a Professor of Mathematics at MIT and an Honorary Fellow of Balliol College.
He was the President of SIAM during 1999 and 2000, and Chair of the Joint Policy Board for Mathematics. He received the von Neumann Medal of the US Association for Computational Mechanics, and the Henrici Prize for applied analysis. The first Su Buchin Prize from the International Congress of Industrial and Applied Mathematics, and the Haimo Prize from the Mathematical Association of America, were awarded for his contributions to teaching around the world. His home page is math.mit.edu/~gs/ and his video lectures on linear algebra and on computational science and engineering are on ocw.mit.edu (mathematics/18.06 and 18.085).

截图:
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注:
1.我会把麻省所有的微积分课程发出来,大约200个视频,有需要的同学请关注。
2.课件:http://ocw.mit.edu/courses/mathematics/18-...terials/,因为官网速度下载较快,这里暂不提供。
3.个人翻译的标题,有啥错误还请慷慨指正.



目录

Lecture 01: The Geometry of Linear Equations
Lecture 02: Elimination with Matrices
Lecture 03: Multiplication and Inverse Matrices
Lecture 04: Factorization into A = LU
Lecture 05: Transposes, Permutations, Spaces R^n
Lecture 06: Column Space and Nullspace
Lecture 07: Solving Ax = 0: Pivot Variables, Special Solutions
Lecture 08: Solving Ax = b: Row Reduced Form R
Lecture 09: Independence, Basis, and Dimension
Lecture 10: The Four Fundamental Subspaces
Lecture 11: Matrix Spaces; Rank 1; Small World Graphs
Lecture 12: Graphs, Networks, Incidence Matrices
Lecture 13: Quiz 1 Review
Lecture 14: Orthogonal Vectors and Subspaces
Lecture 15: Projections onto Subspaces
Lecture 16: Projection Matrices and Least Squares
Lecture 17: Orthogonal Matrices and Gram-Schmidt
Lecture 18: Properties of Determinants
Lecture 19: Determinant Formulas and Cofactors
Lecture 20: Cramer's Rule, Inverse Matrix, and Volume
Lecture 21: Eigenvalues and Eigenvectors
Lecture 22: Diagonalization and Powers of A
Lecture 23: Differential Equations and exp(At)
Lecture 24: Markov Matrices; Fourier Series
Lecture 24b: Quiz 2 Review
Lecture 25: Symmetric Matrices and Positive Definiteness
Lecture 26: Complex Matrices; Fast Fourier Transform
Lecture 27: Positive Definite Matrices and Minimae
Lecture 28: Similar Matrices and Jordan Form
Lecture 29: Singular Value Decomposition
Lecture 30: Linear Transformations and Their Matrices
Lecture 31: Change of Basis; Image Compression
Lecture 32: Quiz 3 Review
Lecture 33: Left and Right Inverses; Pseudoinverse
Lecture 34: Final Course Review

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