## MIT 18.085 Computational Science and Engineering I - Fall 2007

recorded by: Massachusetts Institute of Technology, MIT

released under terms of: Creative Commons Attribution Non-Commercial Share Alike (CC-BY-NC-SA)

released under terms of: Creative Commons Attribution Non-Commercial Share Alike (CC-BY-NC-SA)

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**:

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!!!!!

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.

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.

jim laudon, May 7, 2012 at 7:50 p.m.:hooray doctor strang!

many thanks for the great teaching.

Shakeel Ahmed, October 25, 2013 at 10:53 a.m.:Thanks very much Dr. Strang. Your way of teaching is realy very nice.

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.

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!

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.

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