# click the upper-left icon to select videos from the playlist
source: MIT OpenCourseWare 2009年5月6日
MIT 18.06 Linear Algebra, Spring 2005
Instructor: Prof. Gilbert Strang
This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. *Please note that lecture 4 is unavailable in a higher quality format.
Find more lecture notes, study materials, and more courses at http://ocw.mit.edu.
View the complete course at: http://ocw.mit.edu/18-06S05
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
Lec 1 39:49 The Geometry of Linear Equations.
Lec 2 47:42 Elimination with Matrices.
Lec 3 46:49 Multiplication and Inverse Matrices.
Lec 4 Factorization into A = LU 48:05
Lec 5 47:42 Transposes, Permutations, Spaces R^n.
Lec 6 46:01 Column Space and Nullspace.
Lec 7 43:20 Solving Ax = 0: Pivot Variables, Special Solutions.
Lec 8 47:20 Solving Ax = b: Row Reduced Form R.
Lec 9 50:14 Independence, Basis, and Dimension.
Lec 10 49:20 The Four Fundamental Subspaces.
Lec 11 45:56 Matrix Spaces; Rank 1; Small World Graphs.
Lec 12 47:57 Graphs, Networks, Incidence Matrices.
Lec 13 47:40 Quiz 1 Review.
Lec 14 49:48 Orthogonal Vectors and Subspaces.
Lec 15 48:51 Projections onto Subspaces.
Lec 16 48:05 Projection Matrices and Least Squares
Lec 17 49:25 Orthogonal Matrices and Gram-Schmidt.
Lec 18 49:12 Properties of Determinants.
Lec 19 53:17 Determinant Formulas and Cofactors.
Lec 20 51:01 Cramer's Rule, Inverse Matrix, and Volume.
Lec 21 51:23 Eigenvalues and Eigenvectors.
Lec 22 51:51 Diagonalization and Powers of A.
Lec 23 51:03 Differential Equations and exp(At).
Lec 24 51:12 Markov Matrices; Fourier Series.*
Lec 24b 48:20 Quiz 2 Review. * NOTE: the audio is in the right channel only. If you hear no audio, you are listening only to the left channel.
Lec 25 43:52 Symmetric Matrices and Positive Definiteness. * NOTE: the audio is in the right channel only. If you hear no audio, you are listening only to the left channel.
Lec 26 47:52 Complex Matrices; Fast Fourier Transform.
Lec 27 50:40 Positive Definite Matrices and Minima.
Lec 28 45:56 Similar Matrices and Jordan Form.
Lec 29 41:35 Singular Value Decomposition.
Lec 30 49:27 Linear Transformations and Their Matrices.
Lec 31 50:14 Change of Basis; Image Compression.
Lec 32 47:06 Quiz 3 Review.
Lec 33 41:53 Left and Right Inverses; Pseudoinverse.
Lec 34 43:26 Final Course Review.
Showing posts with label B. (figures)-S-Gilbert Strang. Show all posts
Showing posts with label B. (figures)-S-Gilbert Strang. Show all posts
2016-12-30
Computational Science & Engineering I (Fall 2007 at MIT) by Gilbert Strang at MIT
# click the upper-left icon to select videos from the playlist
source: MIT OpenCourseWare 2008年5月19日
MIT 18.085 Computational Science & Engineering I, Fall 2007
This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.
Note: This course was previously called "Mathematical Methods for Engineers I".
A more recent version of this course is available at: http://ocw.mit.edu/18-085f08
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu
Lec 1 59:51
Lec 2 56:48
Lec 3 57:15
Lec 4 1:07:48
Lec 5 1:07:01
Lec 6 1:05:28
Lec 7 1:07:35
Lec 8 1:05:57
Lec 9 1:09:58
Lec 10 1:00:55
Lec 11 1:06:08
Lec 12 1:06:13
Lec 13 1:11:02
Lec 14 1:00:58
Lec 15 1:06:33
Lec 16 1:02:23
Lec 17 1:05:17
Lec 18 1:07:28
Lec 19 1:08:17
Lec 20 1:01:47
Lec 21 1:09:49
Lec 22 1:02:34
Lec 23 1:15:39
Lec 24 1:00:25
Lec 25 1:22:00
Lec 26 55:22
Lec 27 1:15:50
Lec 28 1:04:34
Lec 29 1:14:04
Lec 30 1:16:30
Lec 31 1:05:08
Lec 32 50:14
source: MIT OpenCourseWare 2008年5月19日
MIT 18.085 Computational Science & Engineering I, Fall 2007
This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.
Note: This course was previously called "Mathematical Methods for Engineers I".
A more recent version of this course is available at: http://ocw.mit.edu/18-085f08
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu
Lec 1 59:51
Lec 2 56:48
Lec 3 57:15
Lec 4 1:07:48
Lec 5 1:07:01
Lec 6 1:05:28
Lec 7 1:07:35
Lec 8 1:05:57
Lec 9 1:09:58
Lec 10 1:00:55
Lec 11 1:06:08
Lec 12 1:06:13
Lec 13 1:11:02
Lec 14 1:00:58
Lec 15 1:06:33
Lec 16 1:02:23
Lec 17 1:05:17
Lec 18 1:07:28
Lec 19 1:08:17
Lec 20 1:01:47
Lec 21 1:09:49
Lec 22 1:02:34
Lec 23 1:15:39
Lec 24 1:00:25
Lec 25 1:22:00
Lec 26 55:22
Lec 27 1:15:50
Lec 28 1:04:34
Lec 29 1:14:04
Lec 30 1:16:30
Lec 31 1:05:08
Lec 32 50:14
2016-12-27
Mathematical Methods for Engineers II (MIT) by Gilbert Strang
# click the up-left corner to select videos from the playlist
source: MIT OpenCourseWare 2008年5月19日
View the complete course at: http://ocw.mit.edu/18-086S06
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu
MIT 18.086 Computational Science & Engineering II
Lec 1 | MIT 18.086 Mathematical Methods for Engineers II 44:42 Difference Methods for Ordinary Differential Equations
Lec 2 55:48
Lec 3 55:43
Lec 4 52:20
Lec 5 54:59
Lec 6 52:17
Lec 7 54:58
Lec 8 53:31
Lec 9 44:30
Lec 10 56:02
Lec 11 53:46
Lec 12 53:59
Lec 13 56:05
Lec 14 49:34
Lec 15 51:34
Lec 16 47:13
Lec 17 51:16
Lec 18 49:34
Lec 19 52:23
Lec 20 48:25
Lec 21 50:56
Lec 22 52:24
Lec 23 51:45
Lec 24 50:25
Lec 25 51:29
Lec 26 52:37
Lec 27 49:18
Lec 28 56:35
Lec 29 51:28
Lecture 1 | Modern Physics: Classical Mechanics (Stanford) 47:50
source: MIT OpenCourseWare 2008年5月19日
View the complete course at: http://ocw.mit.edu/18-086S06
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu
MIT 18.086 Computational Science & Engineering II
Lec 1 | MIT 18.086 Mathematical Methods for Engineers II 44:42 Difference Methods for Ordinary Differential Equations
Lec 2 55:48
Lec 3 55:43
Lec 4 52:20
Lec 5 54:59
Lec 6 52:17
Lec 7 54:58
Lec 8 53:31
Lec 9 44:30
Lec 10 56:02
Lec 11 53:46
Lec 12 53:59
Lec 13 56:05
Lec 14 49:34
Lec 15 51:34
Lec 16 47:13
Lec 17 51:16
Lec 18 49:34
Lec 19 52:23
Lec 20 48:25
Lec 21 50:56
Lec 22 52:24
Lec 23 51:45
Lec 24 50:25
Lec 25 51:29
Lec 26 52:37
Lec 27 49:18
Lec 28 56:35
Lec 29 51:28
Lecture 1 | Modern Physics: Classical Mechanics (Stanford) 47:50
2016-12-23
Computational Science & Engineering I (Fall 2008 at MIT) by Gilbert Strang
# click the up-left corner to select videos from the playlist
source: tawkaw OpenCourseWare 2014年6月6日
MIT 18.085 Computational Science & Engineering I (Fall 2008 at MIT)
This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.
Note: This course was previously called "Mathematical Methods for Engineers I".
View the Complete Course at: ocw.mit.edu/18-085F08
49 Lecture 36 Sampling Theorem 40:58
48 Lecture 35 Convolution equations, deconvolution, convolution in 2D 51:21
47 Recitation 13 50:29
46 Lecture 34 Fourier integral transform part 2 51:27
45 Lecture 33 Filters Fourier integral transform part 1 51:23
44 Lecture 32 Convolution part 2 52:04
43 Recitation 12 51:12
42 Lecture 31 Examples of discrete Fourier transform, fast Fourier transform, convolution part 1 51:42
41 Lecture 30 Discrete Fourier series 50:12
40 Lecture 29 Fourier series part 2 48:41
39 Recitation 11 54:08
38 Lecture 28 Fourier series part 1 49:23
37 Lecture 27 Finite elements in 2D part 2 52:33
36 Recitation 10 45:33
35 Lecture 26 Fast Poisson solver part 2, finite elements in 2D part 1 51:28
34 Lecture 25 Fast Poisson solver part 1 52:22
33 Lecture 24 Laplace's equation part 2 54:21
32 Recitation 09 51:35
31 Lecture 23 Laplace's equation part 1 49:53
30 Lecture 22 Gradient and divergence part 2 51:19
29 Lecture 21 Boundary conditions, splines, gradient and divergence part 1 53:22
28 Recitation 08 48:08
27 Lecture 20 Element matrices 4th order bending equations 50:13
26 Lecture 19 Quadratic cubic elements 52:36
25 Lecture 18 Finite elements in 1D part 2 51:36
24 Recitation 07 53:54
23 Lecture 17 Finite elements in 1D part 1 54:22
22 Lecture 16 Trusses part 2 48:41
21 Lecture 15 Trusses and A^TCA 46:42
20 Recitation 06 54:26
19 Lecture 14 Exam Review 52:30
18 Lecture 13 Kirchhoff's Current Law 54:37
17 Recitation 05 54:54
16 Lecture 12 Graphs and networks 50:28
15 Lecture 11 Least squares part 2 54:00
14 Lecture 10 Finite differences in time, least squares part 1 54:59
13 Recitation 04 56:18
12 Lecture 09 Oscillation 53:27
11 Lecture 08 Springs and masses the main framework 55:14
10 Recitation 03 56:13
09 Lecture 07 Positive definite day! 52:56
08 Lecture 06 Eigenvalues part 2 positive definite part 1 50:19
07 Lecture 05 Eigenvalues part 1 56:12
06 Recitation 02 51:13
05 Lecture 04 Delta function day! 55:39
04 Lecture 03 Solving a linear system 54:40
03 Lecture 02 Difference equations 52:27
02 Recitation 01 Key ideas of linear algebra 49:32
01 Lecture 01 Four special matrices 54:05
Course Introduction 4:12
source: tawkaw OpenCourseWare 2014年6月6日
MIT 18.085 Computational Science & Engineering I (Fall 2008 at MIT)
This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.
Note: This course was previously called "Mathematical Methods for Engineers I".
View the Complete Course at: ocw.mit.edu/18-085F08
49 Lecture 36 Sampling Theorem 40:58
48 Lecture 35 Convolution equations, deconvolution, convolution in 2D 51:21
47 Recitation 13 50:29
46 Lecture 34 Fourier integral transform part 2 51:27
45 Lecture 33 Filters Fourier integral transform part 1 51:23
44 Lecture 32 Convolution part 2 52:04
43 Recitation 12 51:12
42 Lecture 31 Examples of discrete Fourier transform, fast Fourier transform, convolution part 1 51:42
41 Lecture 30 Discrete Fourier series 50:12
40 Lecture 29 Fourier series part 2 48:41
39 Recitation 11 54:08
38 Lecture 28 Fourier series part 1 49:23
37 Lecture 27 Finite elements in 2D part 2 52:33
36 Recitation 10 45:33
35 Lecture 26 Fast Poisson solver part 2, finite elements in 2D part 1 51:28
34 Lecture 25 Fast Poisson solver part 1 52:22
33 Lecture 24 Laplace's equation part 2 54:21
32 Recitation 09 51:35
31 Lecture 23 Laplace's equation part 1 49:53
30 Lecture 22 Gradient and divergence part 2 51:19
29 Lecture 21 Boundary conditions, splines, gradient and divergence part 1 53:22
28 Recitation 08 48:08
27 Lecture 20 Element matrices 4th order bending equations 50:13
26 Lecture 19 Quadratic cubic elements 52:36
25 Lecture 18 Finite elements in 1D part 2 51:36
24 Recitation 07 53:54
23 Lecture 17 Finite elements in 1D part 1 54:22
22 Lecture 16 Trusses part 2 48:41
21 Lecture 15 Trusses and A^TCA 46:42
20 Recitation 06 54:26
19 Lecture 14 Exam Review 52:30
18 Lecture 13 Kirchhoff's Current Law 54:37
17 Recitation 05 54:54
16 Lecture 12 Graphs and networks 50:28
15 Lecture 11 Least squares part 2 54:00
14 Lecture 10 Finite differences in time, least squares part 1 54:59
13 Recitation 04 56:18
12 Lecture 09 Oscillation 53:27
11 Lecture 08 Springs and masses the main framework 55:14
10 Recitation 03 56:13
09 Lecture 07 Positive definite day! 52:56
08 Lecture 06 Eigenvalues part 2 positive definite part 1 50:19
07 Lecture 05 Eigenvalues part 1 56:12
06 Recitation 02 51:13
05 Lecture 04 Delta function day! 55:39
04 Lecture 03 Solving a linear system 54:40
03 Lecture 02 Difference equations 52:27
02 Recitation 01 Key ideas of linear algebra 49:32
01 Lecture 01 Four special matrices 54:05
Course Introduction 4:12
2016-06-23
Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015 at MIT
# Click the up-left corner for the playlist of the 68 videos
source: MIT OpenCourseWare 2016年5月6日/上次更新：2016年5月23日
MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
View the complete course: http://ocw.mit.edu/RES-18-009F15
Instructor: Gilbert Strang, Cleve Moler
Gilbert Strang and Cleve Moler provide an overview to their in-depth video series about differential equations and the MATLAB® ODE suite.
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu
Introduction to Differential Equations and the MATLAB® ODE Suite 2:53
Overview of Differential Equations 14:04
The Calculus You Need 14:47
Response to Exponential Input 13:20
Response to Oscillating Input 15:55
Solution for Any Input 13:59
Step Function and Delta Function 15:41
Response to Complex Exponential 12:51
Integrating Factor for Constant Rate 13:47
Integrating Factor for a Varying Rate 11:23
The Logistic Equation 13:27
The Stability and Instability of Steady States 21:15
Separable Equations 13:07
Second Order Equations 19:20
Forced Harmonic Motion 15:32
Unforced Damped Motion 14:04
Impulse Response and Step Response 16:02
Exponential Response — Possible Resonance 12:20
Second Order Equations with Damping 13:14
Electrical Networks: Voltages and Currents 16:33
Method of Undetermined Coefficients 16:32
An Example of Undetermined Coefficients 15:49
Variation of Parameters 19:22
Laplace Transform: First Order Equation 22:38
Laplace Transform: Second Order Equation 16:31
Laplace Transforms and Convolution 10:29
Pictures of Solutions 21:01
Phase Plane Pictures: Source, Sink, Saddle 18:26
Phase Plane Pictures: Spirals and Centers 13:46
Two First Order Equations: Stability 10:32
Linearization at Critical Points 15:08
Linearization of Two Nonlinear Equations 21:41
Eigenvalues and Stability: 2 by 2 Matrix, A 19:30
The Tumbling Box in 3-D 22:54
The Column Space of a Matrix 12:44
Independence, Basis, and Dimension 13:20
The Big Picture of Linear Algebra 15:57
Graphs 15:27
Incidence Matrices of Graphs 19:51
Eigenvalues and Eigenvectors 19:01
Diagonalizing a Matrix 11:37
Powers of Matrices and Markov Matrices 17:54
Solving Linear Systems 15:48
The Matrix Exponential 15:32
Similar Matrices 14:51
Symmetric Matrices, Real Eigenvalues, Orthogonal Eigenvectors 15:55
Second Order Systems 16:50
Positive Definite Matrices 21:41
Singular Value Decomposition (the SVD) 14:11
Boundary Conditions Replace Initial Conditions 17:03
Laplace Equation 13:17
Fourier Series 16:36
Examples of Fourier Series 13:56
Fourier Series Solution of Laplace's Equation 14:04
Heat Equation 10:48
Wave Equation 15:14
Euler, ODE1 15:22
Midpoint Method, ODE2 6:46
Classical Runge-Kutta, ODE4 9:38
Order, Naming Conventions 5:26
Estimating Error, ODE23 10:37
ODE45 6:47
Stiffness, ODE23s, ODE15s 7:15
Systems of Equations 14:17
The MATLAB ODE Suite 5:35
Tumbling Box 9:52
Predator-Prey Equations 14:17
Lorenz Attractor and Chaos 10:25
source: MIT OpenCourseWare 2016年5月6日/上次更新：2016年5月23日
MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
View the complete course: http://ocw.mit.edu/RES-18-009F15
Instructor: Gilbert Strang, Cleve Moler
Gilbert Strang and Cleve Moler provide an overview to their in-depth video series about differential equations and the MATLAB® ODE suite.
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu
Introduction to Differential Equations and the MATLAB® ODE Suite 2:53
Overview of Differential Equations 14:04
The Calculus You Need 14:47
Response to Exponential Input 13:20
Response to Oscillating Input 15:55
Solution for Any Input 13:59
Step Function and Delta Function 15:41
Response to Complex Exponential 12:51
Integrating Factor for Constant Rate 13:47
Integrating Factor for a Varying Rate 11:23
The Logistic Equation 13:27
The Stability and Instability of Steady States 21:15
Separable Equations 13:07
Second Order Equations 19:20
Forced Harmonic Motion 15:32
Unforced Damped Motion 14:04
Impulse Response and Step Response 16:02
Exponential Response — Possible Resonance 12:20
Second Order Equations with Damping 13:14
Electrical Networks: Voltages and Currents 16:33
Method of Undetermined Coefficients 16:32
An Example of Undetermined Coefficients 15:49
Variation of Parameters 19:22
Laplace Transform: First Order Equation 22:38
Laplace Transform: Second Order Equation 16:31
Laplace Transforms and Convolution 10:29
Pictures of Solutions 21:01
Phase Plane Pictures: Source, Sink, Saddle 18:26
Phase Plane Pictures: Spirals and Centers 13:46
Two First Order Equations: Stability 10:32
Linearization at Critical Points 15:08
Linearization of Two Nonlinear Equations 21:41
Eigenvalues and Stability: 2 by 2 Matrix, A 19:30
The Tumbling Box in 3-D 22:54
The Column Space of a Matrix 12:44
Independence, Basis, and Dimension 13:20
The Big Picture of Linear Algebra 15:57
Graphs 15:27
Incidence Matrices of Graphs 19:51
Eigenvalues and Eigenvectors 19:01
Diagonalizing a Matrix 11:37
Powers of Matrices and Markov Matrices 17:54
Solving Linear Systems 15:48
The Matrix Exponential 15:32
Similar Matrices 14:51
Symmetric Matrices, Real Eigenvalues, Orthogonal Eigenvectors 15:55
Second Order Systems 16:50
Positive Definite Matrices 21:41
Singular Value Decomposition (the SVD) 14:11
Boundary Conditions Replace Initial Conditions 17:03
Laplace Equation 13:17
Fourier Series 16:36
Examples of Fourier Series 13:56
Fourier Series Solution of Laplace's Equation 14:04
Heat Equation 10:48
Wave Equation 15:14
Euler, ODE1 15:22
Midpoint Method, ODE2 6:46
Classical Runge-Kutta, ODE4 9:38
Order, Naming Conventions 5:26
Estimating Error, ODE23 10:37
ODE45 6:47
Stiffness, ODE23s, ODE15s 7:15
Systems of Equations 14:17
The MATLAB ODE Suite 5:35
Tumbling Box 9:52
Predator-Prey Equations 14:17
Lorenz Attractor and Chaos 10:25
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