Solving First-order Linear ODE’s; Steady-state and Transient Solutions. View the complete course: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu

25 thoughts on “Lec 3 | MIT 18.03 Differential Equations, Spring 2006”

ffddssaavvccxxzz

many many many many many many many thaaanks for mit

Satchindra

come on who REALLY understands this stuff? not me.

mindsoulbody

That is the result of chinese professor who can barely speak english and expect student to know everything before even the class started. Welcome to Stony Brook University.

WHEATTHlNS

I find it hard to believe your Professor didn’t explain the Linear DE’s and how to solve them. That would be a Calculus Professor skipping over continuity and jumping right into differentiation.

wasssabii

hes saying n by n matrices

ohmannhey

I donÂ´t think you can get anyway better explained than this …

ahmedgeneral3010

good silence in the lecture ..we have a rock party every lecture

discoinfern0

“since this is gonna be a prime course of confusion..”

haha nice one Prof

mindsoulbody

Now this is what I call lecture. My professor didn’t even say a thing about all these basic stuffs. Awasome, and thanks for posting.

BKproduction1906

wow. man this professor is very good, my professor sucks. :3 man now i can Get a good mark beter than C or C+ XD

Arissef

It was supposed to be “sign of p”, not “sine of p”

michaelfraguada

One thing to add as well. As amazing as is sounds, this phenomena can produce turbulence. The density gradient might be high enough to consider the fluid to behave in the turbulent region. Of course there is a lot more to this subject but I thought it would catch your attention if you were new to it.

michaelfraguada

The convection is totally independent of the conduction, in this example. Even if the cup was a perfect insulator the coffee would transfer heat to the surrounding air ( considering there is no lid on ) because of the density gradient present. Although, the heat transfer mode is considered to be convection there is actually conduction within a small boundary layer.

HurricaneTeen

So are you saying that the initial conductive transfer of heat to the air (in the coffee example) would cause a density gradient in the air and thus cause convection? Or are you saying that they both occur simultaneously (the convection is not a result of the conduction) simply due to the fact that the coffee is denser than air? If the former, I understand what you’re saying. If the latter, I have something interesting to learn

michaelfraguada

Convection can occur while fluids aren’t moving or are quasi static. This is caused by the density gradient between both fluids.
If you think of it, a cup of coffee will normalize to room temperature if let standing in a mug and in a room where no noticeable movement of air air present. In this case there is both convection and conduction, but I hope you get what I’m saying. You could find more info in any text dedicated to convective heat transfer.

HurricaneTeen

It is my understanding that it is only considered convection when the fluid is in motion. In this case, the fluid is static, which would indeed make this conduction.
Am I wrong?

slingbackshooter

is it called “first-order linear” since the function forms a vector space with y, dy/dx and higher order derivatives as components? Functions form vector spaces since they satisfy all 10 axioms and because arbitrary functions are vector spaces (analogous to scalars used in systems of linear equations) and they are multiplied by a dimensional conponent (y, dy/dx and higher order derivatives), they form a vector space. I know that vector spaces can be used to solve for y but I don’t yet know how.

algorithMIT

If you thought this lecture was excellent, Mattuck is even more impressive in person.

He rides his bike every morning to MIT from Brookline ~10 miles, even in the rain/snow

8308613

Thank you for sharing these lectures.
from IRAN.

sikory

in later video’s he seems to talk about end-by-end matrices

ricardotorress43

good class!

sdfgdsgfsdfg

These videos are pretty long and ArthurÂ´s quite slow.
Someone, who wants to learn this stuff faster, ought to watch khan academyÂ´s vids on diff. eq.

danielk320

this man is awesome!!! he knows too many! =D i’m learning diff eq. thanks to him!!!

CiechanPL

I like the ‘sine of x’ instead of ‘sign of x’ in the captioned version 06:52

jangored3

because he does not know nomenclature he is “no good”? your logic is fallible. he knows pure math, not petty things such as names.

many many many many many many many thaaanks for mit

come on who REALLY understands this stuff? not me.

That is the result of chinese professor who can barely speak english and expect student to know everything before even the class started. Welcome to Stony Brook University.

I find it hard to believe your Professor didn’t explain the Linear DE’s and how to solve them. That would be a Calculus Professor skipping over continuity and jumping right into differentiation.

hes saying n by n matrices

I donÂ´t think you can get anyway better explained than this …

good silence in the lecture ..we have a rock party every lecture

“since this is gonna be a prime course of confusion..”

haha nice one Prof

Now this is what I call lecture. My professor didn’t even say a thing about all these basic stuffs. Awasome, and thanks for posting.

wow. man this professor is very good, my professor sucks. :3 man now i can Get a good mark beter than C or C+ XD

It was supposed to be “sign of p”, not “sine of p”

One thing to add as well. As amazing as is sounds, this phenomena can produce turbulence. The density gradient might be high enough to consider the fluid to behave in the turbulent region. Of course there is a lot more to this subject but I thought it would catch your attention if you were new to it.

The convection is totally independent of the conduction, in this example. Even if the cup was a perfect insulator the coffee would transfer heat to the surrounding air ( considering there is no lid on ) because of the density gradient present. Although, the heat transfer mode is considered to be convection there is actually conduction within a small boundary layer.

So are you saying that the initial conductive transfer of heat to the air (in the coffee example) would cause a density gradient in the air and thus cause convection? Or are you saying that they both occur simultaneously (the convection is not a result of the conduction) simply due to the fact that the coffee is denser than air? If the former, I understand what you’re saying. If the latter, I have something interesting to learn

Convection can occur while fluids aren’t moving or are quasi static. This is caused by the density gradient between both fluids.

If you think of it, a cup of coffee will normalize to room temperature if let standing in a mug and in a room where no noticeable movement of air air present. In this case there is both convection and conduction, but I hope you get what I’m saying. You could find more info in any text dedicated to convective heat transfer.

It is my understanding that it is only considered convection when the fluid is in motion. In this case, the fluid is static, which would indeed make this conduction.

Am I wrong?

is it called “first-order linear” since the function forms a vector space with y, dy/dx and higher order derivatives as components? Functions form vector spaces since they satisfy all 10 axioms and because arbitrary functions are vector spaces (analogous to scalars used in systems of linear equations) and they are multiplied by a dimensional conponent (y, dy/dx and higher order derivatives), they form a vector space. I know that vector spaces can be used to solve for y but I don’t yet know how.

If you thought this lecture was excellent, Mattuck is even more impressive in person.

He rides his bike every morning to MIT from Brookline ~10 miles, even in the rain/snow

Thank you for sharing these lectures.

from IRAN.

in later video’s he seems to talk about end-by-end matrices

good class!

These videos are pretty long and ArthurÂ´s quite slow.

Someone, who wants to learn this stuff faster, ought to watch khan academyÂ´s vids on diff. eq.

this man is awesome!!! he knows too many! =D i’m learning diff eq. thanks to him!!!

I like the ‘sine of x’ instead of ‘sign of x’ in the captioned version 06:52

because he does not know nomenclature he is “no good”? your logic is fallible. he knows pure math, not petty things such as names.