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麻省理工開放課程:線性代數 Linear Algebra 英文版 DVD 只於電腦播放
碟片編號:unc0252d
碟片數量:1片
銷售價格:200
瀏覽次數:28985

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碟片介紹

課程介紹:
這個基礎課程主要闡述矩陣理論和線性代數。主題重點放在對在其他學科的有用的法則上面,包括方程組,向量空間,行列式,特徵值,相似性,以及正定矩陣。

導師介紹
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).
目錄:


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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