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Lec 1 | MIT 18.085 Computational Science and Engineering I, Fall 2008 

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Lecture 1: Four special matrices
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26 июн 2024

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@godfreypigott
@godfreypigott Год назад
Description of Videos in this Playlist: (1) Lecture 1: Four Special Matrices (2) Recitation 1: Key ideas of linear algebra (Combining Vectors, Difference Matrix, 3D Space) (3) Lecture 2: Difference equations (4) Lecture 3: Solving a linear system (5) Lecture 4: Delta function day (6) Recitation 2 (General Solution, Boundary Conditions, Initial Values) (7) Lecture 5: Eigenvalues (part 1) (8) Lecture 6: Eigenvalues (part 2); positive definite (part 1) (9) Lecture 7: Positive definite day (10) Recitation 3 (Positive Definite Matrices, Eigenvalues, Orthogonal Matrices, Difference Matrix) (11) Lecture 8: Springs and masses; the main framework (12) Lecture 9: Oscillation (13) Recitation 4 (Boundary Layer, Element Matrix, Finite Element Method, Differential Equations) (14) Lecture 10: Finite differences in time; least squares (part 1) (15) Lecture 11: Least squares (part 2) (16) Lecture 12: Graphs and networks (17) Recitation 5 (Trapezoidal Method, Energy Conservation, Imaginary Eigenvalues, Taylor Series) (18) Lecture 13: Kirchhoff's Current Law (19) Lecture 14: Exam Review (20) Recitation 6 (Trapezoidal Rule, Difference Equation, Orthogonal Matrices, Difference Matrix) (21) Lecture 15: Trusses and A sup T CA (22) Lecture 16: Trusses (part 2) (23) Lecture 17: Finite elements in 1D (part 1) (24) Recitation 7 (Element Matrix, Finite Differences, Non-Linear Problems and Equations) (25) Lecture 18: Finite elements in 1D (part 2) (26) Lecture 19: Quadratic/cubic elements (27) Lecture 20: Element matrices; 4th order bending equations (28) Recitation 8 (Finite Elements for Heat Transfer & Bending, Discontinuous Galerkin) (29) Lecture 21: Boundary conditions, splines, gradient and divergence (part 1) (30) Lecture 22: Gradient and divergence (part 2) (31) Lecture 23: Laplace's equation (part 1) (32) Recitation 9 (Stream Function, Shear Flow, Divergence Theorem) (33) Lecture 24: Laplace's equation (part 2) (34) Lecture 25: Fast Poisson solver (part 1) (35) Lecture 26: Fast Poisson solver (part 2); finite elements in 2D (part 1) (36) Recitation 10 (Rotation, Finite Elements, Laplace's Equation, Weak Forms) (37) Lecture 27: Finite elements in 2D (part 2) (38) Lecture 28: Fourier series (part 1) (39) Recitation 11 (Eigenvalue Problem, Bessel Functions, Linear Elements, Second Degree Elements) (40) Lecture 29: Fourier series (part 2) (41) Lecture 30: Discrete Fourier series (42) Lecture 31: Examples of discrete Fourier transform; fast Fourier transform; convolution (part 1) (43) Recitation 12 (Initial Conditions, Heat Equation, Partial Differential Equations, Fourier Coefficient) (44) Lecture 32: Convolution (part 2); filtering (45) Lecture 33: Filters; Fourier integral transform (part 1) (46) Lecture 34: Fourier integral transform (part 2) (47) Recitation 13 (Fourier Transforms, Fourier Coefficients, Transfer Function, Gibbs Phenomenon) (48) Lecture 35: Convolution equations: deconvolution; convolution in 2D (49) Lecture 36: Sampling Theorem (50) Prof. Gilbert Strang gives an overview of 18.085 Computational Science and Engineering I, Fall 2008.
@owntor1
@owntor1 15 лет назад
This is refreshing. All professors should promote learning as a priority ahead of grades.
@zairoxs
@zairoxs 6 лет назад
I just can't help it but love this guy. His energy is contagious!
@stephensmith8743
@stephensmith8743 11 лет назад
Professors like him are what make the college experience so memorable and makes me so motivated to do well and succeed.
@phononify
@phononify 11 лет назад
Such a friendly, modest teacher ... great !
@yasrinayuliasari9615
@yasrinayuliasari9615 10 лет назад
This is a clear explanation. I just feel like being in the class and listen for explaining from the great Prof. Gilbert Strang. Love it... Thanks for MIT OCW..
@albertmaia7190
@albertmaia7190 6 лет назад
What a great professor and great man, love to watch his lectures
@ManuelMenzella04
@ManuelMenzella04 15 лет назад
It's great to see that this man really likes teaching what he teaches. That's what makes a great teacher.
@sur1kor
@sur1kor 12 лет назад
rare people with these skills.Possibly few of the rarest on this planet a) Highly knowledgeable b) Good skills in explanation c) and most importantly interest in explaining things
@pranaysheshak5931
@pranaysheshak5931 4 года назад
34:23 Prof. Strang - "We can see it by human intelligence" Me - Maybe I don't have human intelligence
@user-px8iy5jj8q
@user-px8iy5jj8q 4 года назад
Thank you for offering this great lecture to us, Professor Strang!
@mitjtl5738
@mitjtl5738 7 лет назад
I love this guy... he seems so enthusiastic...
@monolito8556
@monolito8556 6 лет назад
Thank you very much for these courses MIT staff. pure gold
@tsnaren
@tsnaren 15 лет назад
An amazing learning experience, some of his instinct based recognition skills which he displays are awesome
@mazenezzeddine8319
@mazenezzeddine8319 6 лет назад
Teach you and no to grade you. Some/Many professors must watch these videos to learn teaching and even sciences. A professor that understands what he is explaining
@mmmmmark9751
@mmmmmark9751 2 года назад
What an amazing teacher......the students are so fortunate. I have a copy of all his textbooks.
@sepidehmajd593
@sepidehmajd593 2 года назад
thanks MIT for this great donation to the world especially from the professor of the course to share
@virajkadam3017
@virajkadam3017 2 года назад
Gil is one of the best teacher I know. Thanks to MIT OCW.
@xiatian122
@xiatian122 13 лет назад
MIT provides us foreign college students a path to the courses taken by American undergraduates.Thanks to it,we can manage the skills in understanding the lectures given by American professors in English. I hope I would take the PHD of computer science in MIT in the coming future. Thank you,MIT.
@jtekmmx
@jtekmmx 6 лет назад
Lecture starts at 5:36
@johnson4u
@johnson4u 15 лет назад
It's really great to see such an old professor showing full energy. Beats me. I gotta stop being lazy and put in smart hard work. Btw thanks for the vid.
@LAnonHubbard
@LAnonHubbard 12 лет назад
Thanks for this video. It was getting a bit deep and mysterious for me with the springs, masses and free/fixed discussions but hopefully will make more sense in future lectures...
@fdkfskfkvmk441254741
@fdkfskfkvmk441254741 11 лет назад
He seems to be a very experienced teacher, and very professional.
@AJ_42
@AJ_42 5 лет назад
1.5x is great for his lectures. Huge fan BTW!
@MASTURCHEEF001
@MASTURCHEEF001 12 лет назад
This professor is amazing.
@marisaalves5577
@marisaalves5577 2 года назад
I wanna thank you for being such a good teacher, worried with your students. Marisa, Portugal
@francishubertovasquez2139
@francishubertovasquez2139 3 месяца назад
You said lecturer say something, I said what you're saying shall not be forgotten in memory time by those interested minds in this point in time and hope it won't be cut off by the editor or by the RNA cutters coz it could be transferred to the other side and the effort counts no flattery frankly speaking like the other mindsets doing their thing for what they are like compilations.
@Blueian742
@Blueian742 6 месяцев назад
This dude is great! Id love to have his class. Id be able to really learn and enjoy the content rather than stress about grades. I mean give easy B’s to people who put in the effort and if you do somewhat more than you need you should get an A.
@xXxBladeStormxXx
@xXxBladeStormxXx 12 лет назад
getting good professors is really rare. Most professors of their generation and I mean like 40+ aren't really good. Most students learn from external sources like books and videos made by people who are like 20+ yrs old more than they learn from sitting in classes. I think this generation knows it well how important explaining concepts, going in details, giving real life examples, etc. are and so when our kids will go to colleges the professors might actually be good since they know how it is.
@03Kabbotta11
@03Kabbotta11 12 лет назад
True, and this guy can REALLY teach.
@Kingarthur305
@Kingarthur305 15 лет назад
You got that right, I had a dream of going to MIT a few years ago but I don't need to now. I can continue with my state school and maybe from these lectures go to graduate school at MIT instead of the undergraduate I initially wanted.
@galelio8330
@galelio8330 3 года назад
same here man, but I think I am old now (37 yrs)! do everything you can to reach your dream.
@rrashani
@rrashani 11 лет назад
Thank you for uploading this excellent video. am very lucky at least i could attain partially lecture of such brilliant professor specially regarding one of my interesting subject. Please upload videos as more as possible.
@wa4aos
@wa4aos 13 лет назад
Why not allow life long students above age 50 to actually earn a degree from passing exams related to your online courses. Many of us were unable to complete degrees earlier in life due to pressures of family and financial obligations. Many of us have become successful as self taught business owners. This would be a wonderful contribution to society and in particular to our longer living adults who may have a lot to offer back to society. MIT should take this to the next level. Glenn DSM labs
@jasoncai4769
@jasoncai4769 4 года назад
I love the professor!
@MorningDewPawprint
@MorningDewPawprint 9 лет назад
Holy Moses! Aha you've got to love Prof. Strang
@lukascarter55
@lukascarter55 10 лет назад
Great presentation.
@cwhsu1984
@cwhsu1984 11 лет назад
I would probably spend more time on learning if he was my teacher! The teacher is a really great!
@morone91
@morone91 14 лет назад
he looks like someone who teach with a his heart
@royroci2303
@royroci2303 6 лет назад
thank you to him
@luckyali4948
@luckyali4948 5 лет назад
Very Talented and passionate MIT professor!! My Calculus professor isn't bad but Mechanics professor sucks!, Gf doesn't. even he has got a M-phil in Maths but his way of teaching is 20 years old "writing his notes on the whiteboard in order to solve the textbook questions, then he gives us his solved notes." One can learn Derivatives, Integration and General theorems but the Definite Integrals, Plane Curves and Analytical Geometry of three dimensions doesn't get absorbed in my damn head. Thanks MIT for free stuff!
@augustye3489
@augustye3489 3 года назад
When I looked at the year when the video is recorded, I was kinda worried that the materials might be outdated. God I was wrong.
@moularaoul643
@moularaoul643 3 года назад
Thank you so much!!!!!!
@bevblueroyalpriesthood4361
@bevblueroyalpriesthood4361 6 лет назад
I would like to know whether this is mathematical modeling lecture e.g population models, difference equations and differencial equations? If not where can I find lectures on mathematical modeling?
@hongchulnam1630
@hongchulnam1630 4 года назад
"I shouldn't even tell you this. This is not even interesting" lol
@mohittiwari8934
@mohittiwari8934 5 лет назад
Thanks. MIT 👍
@NoActuallyGo-KCUF-Yourself
@NoActuallyGo-KCUF-Yourself 11 лет назад
Cool stuff!
@Protoex
@Protoex 3 года назад
the mass-spring analogy was let open by context. I guess the key idea is a expression F = -K*X, where: * F is the n x1 matrix of the total forces acting of each of the masses; * X is the n x1 matrix of the positions of each of the masses; * K is the n x n matrix of the system that maps positions to forces produced by the springs. all springs have zero natural length and constant k = 1.
@imranaalam
@imranaalam 2 месяца назад
Excellent
@xtremetom180
@xtremetom180 12 лет назад
really informative and interesting
@cynicdogg2976
@cynicdogg2976 3 года назад
28:37 Its so crazy to think that the precision of computers is not as optimal as we believe them to be.
@sachoslks
@sachoslks 12 лет назад
@lucirz I totaly agree with you!
@muraliday
@muraliday 9 лет назад
What the matrix can be called if the non-zero elements and zero elements are equal? Sparse (for having more zeros) and dense (for having more non-zeros)
@friendly1911
@friendly1911 11 лет назад
There are two versions of the same lecture seris 18.085. Can somebody suggest which one to follow. There are some basic areas missing in computational Science Engineering 1 especially the kalman filter part..
@subramaniannk3364
@subramaniannk3364 4 года назад
How he related mass-spring systems to matrices? I guess I will have to watch again
@jayejayeee
@jayejayeee 12 лет назад
good work here
@tmfelwu
@tmfelwu 5 лет назад
a million by million dense matrix is not a good thing to think about - gilbert strang
@francishubertovasquez2139
@francishubertovasquez2139 3 месяца назад
RNA the couriers of report and implementors of message and have their parallels.
@ashlynnundlall
@ashlynnundlall 8 лет назад
Hi MIT thanks for the previous reply. Please tell me is their an 18.04 and an 18.05 course before the linear Algebra 18.06 course? Thank you
@mitocw
@mitocw 8 лет назад
Multi-variable Calculus 18.02 (ocw.mit.edu/18-02SCF10) is the only pre-req for 18.06.
@dr.merlot1532
@dr.merlot1532 7 лет назад
7/11 was a part time job. What do you think about this MIT OpenCourseWare? In what course will I learn Linear Algebra on the level of Hoffman and Kunze?
@tuo9433
@tuo9433 2 года назад
Can anyone explain the last part, about the system of springs. How does the matrices describe the system of free/fix spring?
@user-ef3ej4pq4f
@user-ef3ej4pq4f 5 лет назад
For those who said "I don't understand this"... As far ad I can tell, this series is one of the BEST tutorials you can find in earth about fourier & other math topics in engineering, If you still cannot understand what he said, that means your math sucks and this is not for you. Stop learning something that you are not going to use in your whole life.
@trungtiennguyendang7624
@trungtiennguyendang7624 5 лет назад
I lost everything when he came to the masses and springs lol
@desjajjaden49
@desjajjaden49 4 года назад
It comes to me that Professor Strang knows everything 😂
@LQGwithLTR
@LQGwithLTR 14 лет назад
@mjolnir1981 正如您所說的,這是研究所的課程唷!
@alienkishorekumar
@alienkishorekumar 13 лет назад
@hollyworldman2 computational science and engineering don't need specific background so anyone can study !!
@martinsanchez-hw4fi
@martinsanchez-hw4fi Год назад
Morally toeplitz made my day
@vhak8706
@vhak8706 11 лет назад
Just watched to see how things are in MIT
@12Alforja
@12Alforja 14 лет назад
Lucirz I am total agree with you. YOU CAN SAID THAT AGAIN!!!!!!!!!!!!! Thanks.
@user-fc7ww7lx4u
@user-fc7ww7lx4u 8 лет назад
这个弹簧惊为天人~~
@firezzzzz
@firezzzzz 12 лет назад
@ForcedToSignUp It is never too late to pick things up.
@luanacibele4261
@luanacibele4261 8 лет назад
Great class, Professor. So glad that MIT is sharing your classes with us =) But, I have one doubt. Why is 1 for when the structure is free and 2 for fixed structure? Is there an explanation for these number?
@TehMaxLightning
@TehMaxLightning 8 лет назад
I'm confused about that too... maybe it's because the point is now connected to one node instead of two?
@luanacibele4261
@luanacibele4261 8 лет назад
+Max Lightning You had a good observation, Max probably, Yes
@TehMaxLightning
@TehMaxLightning 8 лет назад
It's thanks to my Sharingan.
@robertw2930
@robertw2930 7 лет назад
Wolfram-alpha exist at this time ?
@prakhargupta644
@prakhargupta644 4 года назад
Is there any alternative book that would be good for this course and easily available?
@vivekkoul4428
@vivekkoul4428 2 года назад
yes, its : Gilbert Strang - Computational science and engineering-Wellesley-Cambridge Press (2007)
@LChangeTheWorlDS
@LChangeTheWorlDS 11 лет назад
I wonder which degree does this lesson support for?
@moaaltaeb
@moaaltaeb 11 лет назад
I agree with the previous comment
@tchappyha4034
@tchappyha4034 5 лет назад
I love this blue shirt.
@emylrmm
@emylrmm Год назад
I'm assuming this is a 2nd year course, because concepts discussed would be adequately covered in freshman course 18.06 which should be a prerequisite for 18.085
@mjolnir1981
@mjolnir1981 14 лет назад
is that a Msc class or undergraduate? as far as i know in europe computational engineering is a MSc or PhD
@Madsupervilian
@Madsupervilian 11 лет назад
yeah some schools like community college, some proffessors dont care, they purposely fail to teach well. Its easier to become a college professor at my school than teach at a high school. Its all self taught if you take physics, calculus or any other high level college courses.
@KyrychenkoAnton
@KyrychenkoAnton 9 лет назад
may be i'm loosing smth but tell me, in what way is that a mathematical modelling class?
@damnage97
@damnage97 8 лет назад
you use the methods to discretely solve the system numerically. from there you essentially have data sets that can be further analyzed graphically (traditional plots, 3d plots, simulations, etc) by the nature of the question, I don't think u understand mathematical modelling
@q123477
@q123477 15 лет назад
Going to a school such as MIT though almost guarantee you a good job though. It's kind of like buying brand name goods.
@hollyworldman2
@hollyworldman2 13 лет назад
Hi you guys, can anyone from MIT tell me if economic students take this course?
@khairulumam3953
@khairulumam3953 5 лет назад
Can math major use this playlist as resource?
@nolifeonearth9046
@nolifeonearth9046 5 лет назад
for a maths major, you need to go deeper. But for a start this may give you an overview
@LQGwithLTR
@LQGwithLTR 14 лет назад
Prof. Gilbert Strang 您實在太神了! 囧
@pattttttrick
@pattttttrick 13 лет назад
The sound is not loud enough!!!
@pacman7328
@pacman7328 11 лет назад
I wish he was my teacher or i wish I will have him in college
@NDUB10
@NDUB10 15 лет назад
what's with the chalk boards, my high school is using promethean boards to teach.
@davidlovell729
@davidlovell729 7 лет назад
A neanderthal on a promethean board is still a neanderthal. A genius on a chalk board is still a genius. Take your pick.
@tchappyha4034
@tchappyha4034 5 лет назад
I cannot understand his explanation by spring and mass.
@xXxBladeStormxXx
@xXxBladeStormxXx 12 лет назад
Oh and it's so funny when he said "I like to teach you, not to grade you" and "Don't worry about grades" all these other fail professors start every semester with talking about grades and how you should memorize things and focus only on grades. It's hilarious!
@TheMrRedPepper
@TheMrRedPepper 13 лет назад
My dream is to go to MIT, I wish it would come true...
@wazowskisyoutube4152
@wazowskisyoutube4152 3 года назад
are you there?
@TheCuriousCurator-Hindi
@TheCuriousCurator-Hindi 11 лет назад
Its not like any other colllege.. You have not seen bad.. :P We have..
@MMM-wi1mm
@MMM-wi1mm 4 года назад
** WHOAMI IS MY BEST !!
@qbtc
@qbtc 4 года назад
Why is this listed as a graduate level course on MIT/OCW?
@mitocw
@mitocw 4 года назад
It was taught at MIT as a graduate course. It's designed for students who are already engineers.
@SentryandFriends
@SentryandFriends 11 лет назад
I can't stop staring at his winking eye.
@UnforsakenXII
@UnforsakenXII 7 лет назад
CRAMMMINGGGGGG
@brian77771
@brian77771 7 лет назад
you shouldn't be doing that
@UnforsakenXII
@UnforsakenXII 7 лет назад
It paid off. I watch like 50 video lectures every winter break and learn as much before school begins again, lol.
@imegatrone
@imegatrone 12 лет назад
I Really Like The Video Four special matrices From Your
@slatz20
@slatz20 13 лет назад
Our professors in Germany read fucking Books every single week. Its ridicolous. U ARE THE GREATEST Mr. Gilbert Strang.
@HackedPC
@HackedPC 7 месяцев назад
which uni
@halamkajohn
@halamkajohn 10 лет назад
finite element and eigenvalues are elusive to me. actual equations for actual problems are rarely done. CSULB had math both ways. F = KX ? You can see JAMMA boards on EBAY. The computers of today are simpler than FORTRAN computers of 1970 s. COMPILERS would set gate paths ahead of time. Actual circuits wouldf change. In the ghz speed . a lot of back and forth to the same data and address bus can be slow More than 1 data bus was used on the FORTRAN computer. I think the compromise is to make a 500 mhz BASIC computer with just the non paul allen approved microprocessor. SAME as earlier BASIC computers. FLOW chart for writing the program line into memory 1 8 bit character at a time starting with parentheses.
@muadali9465
@muadali9465 9 лет назад
Is computational science and computer science same
@hasnainrehman
@hasnainrehman 8 лет назад
+muad ali Actually no, these are different fields. Computational Science and Engineering (CSE) deals with solving the mathematical problems in Science and Engineering using the power of computers. The pillars of CSE are Numerical Mathematics, Scientific Computing and High Performance Computing. Some of the overlapping areas between CSE and Computer Science are High Performance Computing (like parallel computing, super computing etc), Visualization (Coputer Vision, Simulation), Algorithms (Parallel algorithms, Machine Learning, Big Data) etc.
@muadali9465
@muadali9465 8 лет назад
hasnain rehman thanks man time runs it's been a year when I posted that coment and I still remember
@d.joseph4356
@d.joseph4356 9 лет назад
I wonder how many in that class already knew this stuff going in....
@xXxBladeStormxXx
@xXxBladeStormxXx 7 лет назад
A lot obviously. It's a graduate level class.
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