I need to learn how to solve Laplace Equations by hand by my exam day....HELP!

[beer]

Quick background:

I'm in a 1-semester intro to differential equations course
The book we use focuses mainly on ODEs.

The last 1/3 of the course dealt with partials. I knew what was going on in the class up till that point. As soon as we hit partials, I got lost, and the book became useless.

On the final, I'm pretty sure he is going to have us solve laplace equation, in two dimensions, for a given set of boundary conditions, without the use of any calculator.

I need to figure out how to solve them. Where do I look? No one really knows how to do it reliably...

 

[codeyf]

rofl, glanced at the title and thought it read:

"I need to learn how to solve Lapdance Equations by hand by my exam day....HELP!"

 

[kt]

Your TA? Your professor? They are surprisingly helpful.. I mean, they gotta know what they are teaching right?

Good luck, I remember having to use Laplace's equations many many times in other engineering courses. So, I would suck it up and go to your TA or professor and have a sit down with him/her.

 

[nitsuj3580]

I had all the formulas in my calculator teachers didn't care thank goodness

 

[Random Variable]

I've never heard of a introductory differential equations course that covers ODEs, PDEs, and boundary value problems. That's insane.

 

[beer]

Originally posted by: kt
Your TA? Your professor? They are surprisingly helpful.. I mean, they gotta know what they are teaching right?

Good luck, I remember having to use Laplace's equations many many times in other engineering courses. So, I would suck it up and go to your TA or professor and have a sit down with him/her.

My TA is a first year Ph.D candidate from China. I can barely understand him.

My professor's research is in the area of PDEs and fluid dynamics. I'm not saying he doesn't know the stuff, because he does. I just don't think he can bring it down to the level of the students.

 

[beer]

Originally posted by: Vespasian
I've never heard of a introductory differential equations course that covers ODEs, PDEs, and boundary value problems. That's insane.

We did first, second, and higher order linear homogenous and inhomogenous linear equations.
Then we did power series expansions about an ordinary and singular point, including all possible conditions.
We then went into detail for the heat and wave equation for one dimension. And then we started solving fourier series and then laplace equations.

It's insane.

EDIT: Never allowed to touch a calculator or a computer.

 

[eLiu]

Shoot, if this was next fall, I could help you...I too am taking an intro level course in Difeq, but ours does not cover PDEs. They're in the book, but not part of the curriculum...the next class concentrates exclusively on them though. Sorry man...too bad these aren't simple laplace transformations...those were easy, haha.

-Eric

edit: dude, i want to trade classes w/you...ours moves so slowly

 

[Random Variable]

Originally posted by: Elemental007

Originally posted by: Vespasian
I've never heard of a introductory differential equations course that covers ODEs, PDEs, and boundary value problems. That's insane.

We did first, second, and higher order linear homogenous and inhomogenous linear equations.
Then we did power series expansions about an ordinary and singular point, including all possible conditions.
We then went into detail for the heat and wave equation for one dimension. And then we started solving fourier series and then laplace equations.

It's insane.

EDIT: Never allowed to touch a calculator or a computer.

Fourier series and wave equations should not be covered in a introductory differential equations course. That's crazy.

And we were always allowed to use a Laplace transform table.

 

[dighn]

Originally posted by: Elemental007
Quick background:

I'm in a 1-semester intro to differential equations course
The book we use focuses mainly on ODEs.

The last 1/3 of the course dealt with partials. I knew what was going on in the class up till that point. As soon as we hit partials, I got lost, and the book became useless.

On the final, I'm pretty sure he is going to have us solve laplace equation, in two dimensions, for a given set of boundary conditions, without the use of any calculator.

I need to figure out how to solve them. Where do I look? No one really knows how to do it reliably...

try the methcaod called the seperation of variables, then you apply the boundary conditions and stuff and solve fourirer series

it's pain unless thye make it easy

 

[kt]

Originally posted by: Elemental007

Originally posted by: kt
Your TA? Your professor? They are surprisingly helpful.. I mean, they gotta know what they are teaching right?

Good luck, I remember having to use Laplace's equations many many times in other engineering courses. So, I would suck it up and go to your TA or professor and have a sit down with him/her.

My TA is a first year Ph.D candidate from China. I can barely understand him.

My professor's research is in the area of PDEs and fluid dynamics. I'm not saying he doesn't know the stuff, because he does. I just don't think he can bring it down to the level of the students.

It's still better than having one of us trying to explain it thru this thread. At least with either one of them, you get instant feedback to your questions. No point sitting here waiting for something to fall on your lap. Be a little more proactive and go to their office hours and get the answers you need. Chances are there are a lot of other people asking the same questions, so all you have to do is be there and soak up the materials.

I don't know why a lot of students don't take advantage of professor's and TA's office hours. You probably learn more just spending 15 minutes with them during office hours than a whole week of lectures.

 

[gwlam12]

what the heck? i didnt even know you couold do it with ur calculator. u guys gotta stop depending on your calculator

 

[eakers]

seperation of variables

 

[LordSnailz]

ah ... the fond memories of college ... laplace equations use to be one of my favs. too bad it's almost been 3yrs since graduation ... if I get some time tonight I can give you a quick run through(gotta dig up my book), it's actually not too bad ...

why aren't studying with friends?

 

[beer]

Originally posted by: LordSnailz
ah ... the fond memories of college ... laplace equations use to be one of my favs. too bad it's almost been 3yrs since graduation ... if I get some time tonight I can give you a quick run through(gotta dig up my book), it's actually not too bad ...

why aren't studying with friends?

No one has any clue how to do this kind of stuff. A month ago we hadn't even seen a PDE. Everyone that I know is equally lost, simply because the professor lectures 100% theoretical and then furthermore, the book, which was good for ODE, sucks for PDEs. It doesn't give us enough examples. One example per section is worthless.

On our homework, we've basically been given equations for coefficients of fourier series, but we are expected to show derivations in the final.

60% of the final will be ODE, and easy. It's going to be 5 questions, and 2 hours. One will be sucessive picard iterations for approximation; one will be a variation of paramters, and one will be a power series, or a higher order linear equation involving a wronksian proof and Abel's theorem.

The other two wil be PDE. I'm 100% sure one will be a Laplace, and the other is up for a guess.

 

[eakers]

i am sure that your college library has many books on pdes

go find a good one.

 

[melly]

Originally posted by: Elemental007
Quick background:

I'm in a 1-semester intro to differential equations course
The book we use focuses mainly on ODEs.

The last 1/3 of the course dealt with partials. I knew what was going on in the class up till that point. As soon as we hit partials, I got lost, and the book became useless.

On the final, I'm pretty sure he is going to have us solve laplace equation, in two dimensions, for a given set of boundary conditions, without the use of any calculator.

I need to figure out how to solve them. Where do I look? No one really knows how to do it reliably...

i don't even know what any of this means. is this for calculus or physics? what is the point of solving these equations. what is it trying to determine?

 

[Drakkon]

laplace equations by hand? thats really expecting quite a bit from a 1st semester diff eq class...PDE's arent easy things...and by calculator is easy(plugin formulas)...but by hand is way beyong the scope of just defining in a thread i would think. I remeber that how i learned em (calc first...by hand later). The first place I'd look is on mathforums.com and see if anyone asked a question like yours yet. If not the next best place would be your prof...and if he wont work go look for some assitance at like a learning center on campus (they have em where i go at least) and sometimes theres math majors there who know something...
I'll be realistic though...If you aint got it by now your not gunna get it....so hopefully you got enough to get partial credit on a test....

 

[beer]

Originally posted by: Drakkon
laplace equations by hand? thats really expecting quite a bit from a 1st semester diff eq class...PDE's arent easy things...and by calculator is easy(plugin formulas)...but by hand is way beyong the scope of just defining in a thread i would think. I remeber that how i learned em (calc first...by hand later). The first place I'd look is on mathforums.com and see if anyone asked a question like yours yet. If not the next best place would be your prof...and if he wont work go look for some assitance at like a learning center on campus (they have em where i go at least) and sometimes theres math majors there who know something...
I'll be realistic though...If you aint got it by now your not gunna get it....so hopefully you got enough to get partial credit on a test....

We've only spent a month on partials. I have two weeks to the final, with no class, and no really hard finals. This is the only one I'm having to work my ass off on. I CAN get Laplace equations, they're not beyond my ability. I learned all of multivariable calculus in basically two ngihts and made an A in a sequence, series, and multivar course (two semesters crammed into one).

My university's engineering dept puts a great deal of stress on the math dept to get us learning this crap freshman year. That way, when we take a signals course next spring, we already know enough about linear algebra and diff eq to do well.

 

[SCSIfreek]

If you happen to know a friend that is taking the fundamental examination (EIT). Get his book and go through it, I'm sure you'll find many examples on Laplace Equations and methods in solving it. Thats how i got through my EIT IIRC. Good luck. Just remember the formula and apply it.



--Scsi

 

[jahawkin]

Originally posted by: Elemental007

Originally posted by: LordSnailz
ah ... the fond memories of college ... laplace equations use to be one of my favs. too bad it's almost been 3yrs since graduation ... if I get some time tonight I can give you a quick run through(gotta dig up my book), it's actually not too bad ...

why aren't studying with friends?

No one has any clue how to do this kind of stuff. A month ago we hadn't even seen a PDE. Everyone that I know is equally lost, simply because the professor lectures 100% theoretical and then furthermore, the book, which was good for ODE, sucks for PDEs. It doesn't give us enough examples. One example per section is worthless.

On our homework, we've basically been given equations for coefficients of fourier series, but we are expected to show derivations in the final.

60% of the final will be ODE, and easy. It's going to be 5 questions, and 2 hours. One will be sucessive picard iterations for approximation; one will be a variation of paramters, and one will be a power series, or a higher order linear equation involving a wronksian proof and Abel's theorem.

The other two wil be PDE. I'm 100% sure one will be a Laplace, and the other is up for a guess.

Does that book happen to be Boyce + DiPrima?
I took the ODE/PDE course twice during undergrad. Didn't come close to understanding Laplace till the second time around. I would suggest getting some books from the library that go through Laplace transforms with more examples and more depth. Go through the examples (starting with the most simple) step by step. IIRC, once you get the basic concept down they become pretty easy (easy being a very relative term). Get good at doing separation of variables problems, cause I think you need that technique for most Laplace transforms.

 

[narzy]

your screwed.

 

[beer]

Originally posted by: jahawkin

Originally posted by: Elemental007

Originally posted by: LordSnailz
ah ... the fond memories of college ... laplace equations use to be one of my favs. too bad it's almost been 3yrs since graduation ... if I get some time tonight I can give you a quick run through(gotta dig up my book), it's actually not too bad ...

why aren't studying with friends?

No one has any clue how to do this kind of stuff. A month ago we hadn't even seen a PDE. Everyone that I know is equally lost, simply because the professor lectures 100% theoretical and then furthermore, the book, which was good for ODE, sucks for PDEs. It doesn't give us enough examples. One example per section is worthless.

On our homework, we've basically been given equations for coefficients of fourier series, but we are expected to show derivations in the final.

60% of the final will be ODE, and easy. It's going to be 5 questions, and 2 hours. One will be sucessive picard iterations for approximation; one will be a variation of paramters, and one will be a power series, or a higher order linear equation involving a wronksian proof and Abel's theorem.

The other two wil be PDE. I'm 100% sure one will be a Laplace, and the other is up for a guess.

Does that book happen to be Boyce + DiPrima?
I took the ODE/PDE course twice during undergrad. Didn't come close to understanding Laplace till the second time around. I would suggest getting some books from the library that go through Laplace transforms with more examples and more depth. Go through the examples (starting with the most simple) step by step. IIRC, once you get the basic concept down they become pretty easy. Get good at doing separation of variables problems, cause I think you need that technique for most Laplace transforms.

That is the book

It seems they just didn't give a damn about partials at all. I could hae used the book flawlessly during the ODE part of the course...it was awesome! But the first PDE chapter sucks ass.

EAKERS, do you know any good books in particular? That's kind of why I started this thread. There are probably only a few good books on PDEs....seeing if anyone knew any.

 

[stonecold3169]

I just took my diff eq final monday night... if you need a hand with the transforms, I'll help you... the ones you seem to be having problems with seem to be Heaviside problems, where it gives you something like:
Y^2 - 4Y +2 = { 2 t<2
3 t>=2}

That sorta thing... if you still need help, PM me or contact me over aim, kennyfrancisGK

 

[Triumph]

Originally posted by: Elemental007

Originally posted by: Vespasian
I've never heard of a introductory differential equations course that covers ODEs, PDEs, and boundary value problems. That's insane.

We did first, second, and higher order linear homogenous and inhomogenous linear equations.
Then we did power series expansions about an ordinary and singular point, including all possible conditions.
We then went into detail for the heat and wave equation for one dimension. And then we started solving fourier series and then laplace equations.

It's insane.

EDIT: Never allowed to touch a calculator or a computer.

wtf? sounds like your teacher doesn't know the standard american curriculum. we didn't do any non-homogeneous equations. series was covered under multivariable calculus, not diffeq.

Laplace transforms are awesome, but there's a reason that there are solution tables for them readily available. As an integral excercise, it really depends on how hard the equation is to begin with, I guess...