Direction Fields | MIT 18.03SC Differential Equations, Fall 2011

Direction Fields
Instructor: David Shirokoff
View the complete course: ocw.mit.edu/18-...
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
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[@georgesadler7830]

Professor David Shirokoff, thank you for another great lecture on Direction Fields and Isoclines in Differential Equations.

[@fawzyhegab]

thank you MIT for offering this for FREE!

[@BuddyNovinski]

When I took differential equations (probably before Dave was even born), we NEVER discussed isoclines. Maybe now I'll understand differential equations!

[@ax2kool]

He completed the square. So y^2 + y/m + (1/2m)^2 - (1/2m)^2. Now you can factor the first three terms and take the fourth term to the other side. :)

[@claudiorebelo]

Clear, consice and relevant :) my favorite combination! Thanks!

[@JasonMcguiness]

Wow, it's so simple, i can't believe i didn't understand this sooner.

[@yeslinsequeira4612]

according to the theorem, Id assume we'd need to check for continuity of df(x,y)/dy, particularly at the y=0 integral curve, right? If we could confirm that, we could rigourously show that that y=0 is a boundary to all curves above. I dont trust my sketiching skills enough to be convinced about part 2 of the problem.

[@endogeneticgenetics]

Isn't y' undefined at the origin? (0/0) . Doesn't that prevent the nullcline from being continuous and prevent it from being a solution?

[@izzapz]

You could rearrange the equatuon so that nota having division bit multiplicación by zero?

[@yeslinsequeira4612]

The theorem does not say what happens if the conditions are not met. It only says, if the conditions ARE met, the theorem is useful

[@danieltambunan9717]

So basically, y’ is a function of multivariable and isocline is analog to contour plot, right?

[@josetecnopirobo7058]

Thanks, nice lecture

[@giovannifoulmouth7205]

it's really hard to draw a solution curve on this direction field

[@chaoticoli09]

The thing I still struggle with is drawing accurate solution curves.

[@spontaneousgemini601]

@3:00 he says he combined y^2+(1/m)y together.. how did he get (y+(1/m))^2? I know this might be a simple algebra step.. but I'm confused..

[@abus6749]

I dont understand why nullclines don't always have to be solutions to the equation. Aren't all isoclines, by definition, supposed to be solutions to the equation? Isn't a direction field just the space of all possible solutions to the equation, ie, all possible isoclines? Please help.

[@ClonerD]

If i understand your questions correctly: all isoclines are POSSIBLE solutions to the equation, but not necessary THE (particular) solution of the equation.

[@yeslinsequeira4612]

No, isoclines are NOT solutions. They are curves where the slope in the direction field is constant. In this case, it happens to be that the isocline is also a solution curve. This happened I believe, because the isocline & the slope values are completely the same/in sync. Youre confusing integral curves with isolcilnes. There 2 distinct things, not the same.

[@TheIamwalruss]

@spontaneousgemini601 he used complete the square?? hwat?

[@engruby8]

First, thank you veryyyy much, Second, I neee help urgently.. I can'nt draw the slope of isoclines anymore, never Sometimes doctor and you draw it perpindicular and sometimes no I can't understand the concept E.g., the upper circle's slope is drawn and the lower is inverse, why? And if it should be perpindicular, perpindicular for what? Thank you

[@amorphous8826]

the problem which professor discussed in lecture was a special case where we get the direction field perp to the isolcline...but its not a theorem that it will always be perpendicular. in genearl to draw these direction field, S1;- Draw the level curve by taking y'=C S2;- on random points on that level curve draw a small line of slope C

[@Azevedo2001]

I miss differential equations :(

[@gary1679]

I want to go to MIT

[@billnolastname5078]

I would have already known this if I went to a good school.

[@shashankkeshav7907]

Bill Nolastname Not such If you had interest then only..... Don't blame Be Responsible

[@jeddaaah]

I had my B.S degree in math at Yale, masters degree in math at MIT, and my phd at Harvard..

[@MyNaMeJaC007]

And then you crashed...

[@ahaanbhosale5270]

+NolA BigFan So?

[@jeddaaah]

Ahaan Bhosale just saying, cuz he wasted my time explaining some shit Ive been known since I was lil

[@chefdeputas]

so why did you click the video

[@jigartalaviya2340]

@@jeddaaah Four year late but you r the example of how to go to these schools and still be a total dumbass.

[@spontaneousgemini601]

OmG.. I'm so stupid.. nvm

[@grandorottcod1]

no man, we are not mit's brainiacs. Explain it in an easier way. You were not clear in a lot of things such as why the solution curve comes out to be that shape.

[@SilverArro]

If you watched the lecture that accompanies this recitation and actually understood it, his explanation was perfectly clear. His solution curve was only a rough sketch, so it need not look EXACTLY like that. The point is that it roughly followed the line elements and that it can never cross the x-axis. Again, if you watched the lecture, you would understand why this is so. Review the material and try again; don't blame the instructor. He did just fine. The only part where he perhaps went a bit quickly was in completing the square, but since that was just an algebra step, there was no reason for him to dwell on it.

[@njeridiva85]

break it down for dummies man.

[@SilverArro]

+njeridiva If you're that much of a dummy, perhaps you're using the wrong method of learning ODE's. This lecture was perfectly clear.

[@njeridiva85]

Arlo I found a better instructor on yt who doesn't skip steps... Thanks