## MIT 18.03 Differential Equations - Spring 2006

recorded by: Massachusetts Institute of Technology, MIT

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

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams.

**Course Homepage** 18.03 Differential Equations Spring 2006

**Course features at MIT OpenCourseWare page**:

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**Complete MIT OCW video collection at MIT OpenCourseWare - VideoLectures.NET**

## Unit I: First Order Differential Equations | ||||

## Unit II: Second Order Constant Coefficient Linear Equations | ||||

## Unit III: Fourier Series and Laplace Transform | ||||

## IV: First-order Systems | ||||

Abel Gamarra Osorio, March 28, 2009 at 2:16 a.m.:The courses are super. They are usefull.

Xianben Zhu, April 8, 2009 at 5:52 p.m.:I deeply honor MIT for providing these wonderful resource.

Dr. Mattuck is awesome!

D.Raju, July 4, 2009 at 8:23 a.m.:i know a new concept from above class

gao cao, October 6, 2009 at 1:40 p.m.:I'm very grateful that MIT gives me an opportunity to attend these wonderful classes.

Daniel Taylor, October 22, 2009 at 1:04 a.m.:the opportunity to take Dr. Mattuck's 18.03 class, while floating here on my sailboat is a true gift. I am feeling very thankful for this .. you will find my contribution forthcoming.

very sincere appreciation and thanks proferred ...

daniel taylor

San Juan Island, Wa.

mesut türk, November 1, 2009 at 8:49 p.m.:mr Arthur Mattuck thanks a lots. in turkish "eline sağlık" :)

Chirag, November 3, 2009 at 1:41 p.m.:Hi this is Chirag Jani from India.

I m very thankful to MIT in general & to Mathematics Department & Prof. Arthur Mattuck for sharing such valuable resources with me.

I will contribute to MIT.

张琪, December 5, 2009 at 4:21 a.m.:It's pretty pretty good,I really appreciate it that MIT provide such a perfect chance to learn something about foreign education,and,of course,about differential equation,sincere thanks to you, MIT

Anand Desai, December 12, 2009 at 3:08 a.m.:It's Superb.Thanks to MIT

nino, December 27, 2009 at 1:40 p.m.:Professor arthur is excellent. He is among few rare guys i have seen who can model differential equations so well

Pantel, March 21, 2010 at 12:33 p.m.:I download the lecture file, mp4,or flv , but I cannot see any captions.

Where are the subtitles file ?

If there are in the same file (included) with which player can we see them ?

El Baraka, April 1, 2010 at 1:03 a.m.:All these free courses videos are a revolution in teaching mathematics. Thank you very much.

pourabbassi, September 2, 2010 at 5:01 p.m.:Dear Sirs,

That's great!

I'm an Iranian civil engineer and I really was interested in educating Math. course especially in that university and appreciate that MIT provided such a perfect chance for us.

Thanks a lot to all of you, MIT and especially Prof. Arthur Mattuck.

sincerely yours

Ch Kazakidis, September 7, 2010 at 5:57 p.m.:I want to express my deep appreciation for what MIT offers to the world.

shouket ali, November 10, 2010 at 6:22 p.m.:It has opened a new ray of hope for me to get high-level and high-quality education. Before these online lectures it was just a dream for students like me which belong to developing countries. I am really thankful to MIT for their invaluable services to human kind independent of their origin, religion and caste. I wish this service may continue for infinite time. Specially I want to say thanks to my spiritual teacher Arthur Mattuck.

M>S, November 23, 2010 at 7:40 p.m.:Thanks a lot MIT, I really found your OCW a perfect guide to success. Thanks again :)

wes wortman, February 7, 2011 at 7:51 p.m.:I was looking for solving ODE using Frobenius Method and solving ODE with variable coefficients. Is this actually here somewhere? Its all very good.

Nicanor Buenconsejo Jr, April 21, 2011 at 5:49 a.m.:Thanks to MIT for putting up these video courses.

I have been teaching DE for a long time, yet i can still learn much from Professor Mattuck's way of explaining and developing the concepts. He's great.

Aqeel Hussain, September 4, 2011 at 9:03 a.m.:I want to express my deep appreciation for what MIT offers to the real world, including to all poor country people for distance learning at home and their free time.

Aqeel hussain

ahmed rowaey, September 7, 2011 at 2:03 p.m.:thanks to MIT very much

Nikhil, February 9, 2012 at 8:19 p.m.:Really Great Endeavor for people who are trying to get some of the math into their research!.....

reza, July 31, 2012 at 2:03 p.m.:Thanks they are very well

fernando, October 22, 2012 at 3:51 p.m.:the videos are very usefull.

thank u very much.

Dr.S.Narayana Iyer, November 7, 2012 at 7:45 a.m.:Prof Mattuck's way of lecture is marvellous. A very fine lecture giving lot and lots of information. Every mathematics teacher should learn one important lesson: Mathematics should be taught this way so that students can appreciate. Now-a-days studens run away from Mathematics out of fear. If there is one Mattuck or one Gilbert Strang in every college each and every student/teacher will love Mathematics.

nipun kumar, March 20, 2013 at 3:33 p.m.:thanks a lot. i owe to mit.

Piyush Itankar, May 19, 2014 at 12:38 p.m.:Saved me from getting lost into the wild. The world is better because of you.

Thank you!

KAMAL NASA, November 3, 2015 at 6:47 p.m.:thanks MIT ,