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MIT 18.085 Computational Science and Engineering I - Fall 2007

MIT 18.085 Computational Science and 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".

Course Homepage 18.085 Computational Science and Engineering I Fall 2007

Course features at MIT OpenCourseWare page:

Categories
 [syn]  26319 views, 59:51   Lecture 1: Positive definite matrices K = A'CALecture 1: Positive definite matrices K = A'CA Gilbert Strang Gilbert Strang [syn]  10496 views, 57:15   Lecture 3: Network applications: A = incidence matrixLecture 3: Network applications: A = incidence matrix Gilbert Strang Gilbert Strang [syn]  8810 views, 1:05:27   Lecture 6: Underlying theory: applied linear algebraLecture 6: Underlying theory: applied linear algebra Gilbert Strang Gilbert Strang [syn]  10856 views, 1:09:57   Lecture 9: Solutions of Laplace equation: complex variablesLecture 9: Solutions of Laplace equation: complex variables Gilbert Strang Gilbert Strang 3 comments [syn]  13001 views, 1:00:55   Lecture 10: Delta function and Green's functionLecture 10: Delta function and Green's function Gilbert Strang Gilbert Strang 2 comments [syn]  8045 views, 1:06:07   Lecture 11: Initial value problems: wave equation and heat equationLecture 11: Initial value problems: wave equation and heat equation Gilbert Strang Gilbert Strang 1 comment [syn]  32231 views, 1:02:22   Lecture 16: Dynamic estimation: Kalman filter and square root filterLecture 16: Dynamic estimation: Kalman filter and square root filter Gilbert Strang Gilbert Strang 2 comments [syn]  11312 views, 1:01:47   Lecture 20: Finite element method: equilibrium equationsLecture 20: Finite element method: equilibrium equations Gilbert Strang Gilbert Strang [syn]  7811 views, 1:09:48   Lecture 21: Spectral method: dynamic equationsLecture 21: Spectral method: dynamic equations Gilbert Strang Gilbert Strang [syn]  9396 views, 1:02:33   Lecture 22: Fourier expansions and convolutionLecture 22: Fourier expansions and convolution Gilbert Strang Gilbert Strang [syn]  13429 views, 1:15:38   Lecture 23: Fast fourier transform and circulant matricesLecture 23: Fast fourier transform and circulant matrices Gilbert Strang Gilbert Strang 1 comment [syn]  10812 views, 1:00:24   Lecture 24: Discrete filters: lowpass and highpassLecture 24: Discrete filters: lowpass and highpass Gilbert Strang Gilbert Strang [syn]  9724 views, 1:21:59   Lecture 25: Filters in the time and frequency domainLecture 25: Filters in the time and frequency domain Gilbert Strang Gilbert Strang [syn]  9937 views, 55:21   Lecture 26: Filter banks and perfect reconstructionLecture 26: Filter banks and perfect reconstruction Gilbert Strang Gilbert Strang [syn]  30062 views, 1:15:49   Lecture 27: Multiresolution, wavelet transform and scaling functionLecture 27: Multiresolution, wavelet transform and scaling function Gilbert Strang Gilbert Strang 2 comments [syn]  11864 views, 1:04:34   Lecture 28: Splines and orthogonal wavelets: Daubechies constructionLecture 28: Splines and orthogonal wavelets: Daubechies construction Gilbert Strang Gilbert Strang 1 comment [syn]  12250 views, 1:14:04   Lecture 29: Applications in signal and image processing: compressionLecture 29: Applications in signal and image processing: compression Gilbert Strang Gilbert Strang 2 comments [syn]  21317 views, 1:05:07   Lecture 31: Simplex method in linear programmingLecture 31: Simplex method in linear programming Gilbert Strang Gilbert Strang [syn]  12262 views, 50:13   Lecture 32: Nonlinear optimization: algorithms and theoryLecture 32: Nonlinear optimization: algorithms and theory Gilbert Strang Gilbert Strang

1 mike smith, February 23, 2009 at 2:33 p.m.:

These lectures are good , but this guy Gilbert has some problem with the presentation. He needs write the notes on the board clearly and with some kind of order! Also most of the time you cannot read what the prof is writing because the camera is out of focus?? What is the point? Gilbert is very good though but as usual there are problems getting the info to the student. During the lecture it seems that the camera man is too focused on getting the prof in the shot and not what he is writing, I need to see what he is writing!!!!!

2 Ryan McGoff, December 9, 2010 at 2:44 a.m.:

Dr. Strang is an excellent professor. I enjoy his approach to math which is similar to a mystery novel. It allows students to fall into the mindset and thought process needed, and the focus is always on concept.

3 R.Ayyappan, October 2, 2011 at 8:26 a.m.:

I looked already on Highlights of Calculus & Linear Algebra. They are very good. I suggest few improvement with this course, as well.

1. Post editing - voice enhancement for video by signal processing is required.

2. Poor video camera is used for taking his video, in general. Retake is required with good video camera.

3. Few instance professor confused, whether he is on right track. (This is common some time).Such scene can be removed in the web presentation. It will enhance Prof's presentation to internet viewers. Post video editing is not done with his video, may be due to fund restriction.

I thank MIT & Gilbert for their continued effort. Such improvement will help other regional translators. Example: Mixing local language with english will give better learning for non-english speakers. Chinese are translating now-a-days. Other governments will also come forward, provided the royalty is less. In my state(India, Tamilnadu state), our political parties are giving much importance improving the "Tamil" language in technical knowledge. It seems that their efforts are hampered by high royalty fees.

4 jim laudon, May 7, 2012 at 7:50 p.m.:

hooray doctor strang!
many thanks for the great teaching.

5 Shakeel Ahmed, October 25, 2013 at 10:53 a.m.:

Thanks very much Dr. Strang. Your way of teaching is realy very nice.

6 Sania, March 28, 2014 at 2:39 p.m.:

All of Professor Gilbert's videos on any subject related to Mathematics are informative and worth to be watched. He mainly focuses on explaining ideas and concepts rather than merely solving questions. This is something really indispensable to well comprehend Mathematics and related topics.
Making such invaluable videos freely available for people present in any corner of the world is certainly a great breakthrough and efforts made by team member are simply commendable.
I love to watch educational videos designed by OCW team and appreciate their struggle. Finally, I humbly request MIT to post videos on variety of highly important Mathematics subjects such as Number Theory, Basics of Functional Analysis, Measure Theory, Topology, Numerical Analysis, Descriptive and Inferential Statistics, Ordinary and Partial Differential Equations (Theory and Applications), Numerical Linear Algebra, Numerical Techniques and Their Analysis to solve ODEs and PDEs,Laplace and Fourier Transforms, Complex Variables, Research Methodology, How to write a persuasive research paper, and etc.

7 Mikhail Shvartsman, April 23, 2014 at 4:14 p.m.:

Lecture 18 is a masterpiece, probably a semester worth of information in one lecture! Superb!

8 Xiao Yu, June 13, 2014 at 5:14 a.m.:

Thanks for giving these valuable and helpful information and knowledge to us. It's best course I have ever took. Professor Strang is the best teacher I have ever met. I hope more and more students and even teachers can get benefit for the MIT opencourse plan.

9 Patrick Sweetman, August 9, 2015 at 3:24 a.m.:

function R=make_invK(n)
%
% For MIT-18085 lecture 1
% Make inverse of K array
% 09/08/2015 Patrick Sweetman
%
% K array is a square array with a
% diagonal of 2s with -1s on either side.
%
% eg. make_invK(4)
% 0.8 0.6 0.4 0.2
% 0.6 1.2 0.8 0.4
% 0.4 0.8 1.2 0.6
% 0.2 0.4 0.6 0.8
%
% make_invK(4)^-1
% 2 -1 0 0
% -1 2 -1 0
% 0 -1 2 -1
% 0 0 -1 2

R=zeros(n);
for row=1:n
for col=1:n
R(row+n*col-n)=(n+1)*col-row*col-(n+1)*col*(row<col)+(n+1)*row*(row<col);
end
end

R=R/(n+1);

end