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#26 Re: Help Me ! » Integrating a second derivative » 2011-11-07 20:16:36

lindah

Ah,
the constant of integration is a function of all other variables of the partial derivative.

#27 Help Me ! » Integrating a second derivative » 2011-11-06 12:38:20

lindah
Replies: 2

Hi guys,

It has been a while. I was traveling along swimmingly with this subject but have hit a rock!

May I ask how I would integrate the following with working:

and obtain the following answer


Where F and G are arbitrary twice differentiated functions

Thank you in advance for any tips given!

#28 Re: Help Me ! » Separation of variables: DE » 2011-09-24 00:44:40

lindah

Hi bobbym;

Sorry about that!
I'm having my blonde moments (its late here) and dreaming of nothing but differential equations atm

#29 Re: Help Me ! » Power Series solution » 2011-09-24 00:29:40

lindah

Hi zetafunc.

Thank you for the suggestion!!! I am currently working with Airy and Biry functions, as well as Bessel functions.
In setting the assignment, my lecturer has decided to throw curve balls to put us in our place!!!

#30 Re: Help Me ! » Separation of variables: DE » 2011-09-24 00:26:44

lindah

Alternative working for this question as I am writing up my final atm

I'm curious as to why ln|w-2| also works, and this time around, instead of using integration by parts, I also do not have the +3 like bob initially.

#31 Re: Help Me ! » Power Series solution » 2011-09-23 12:18:10

lindah

Hi bobbym;

Sorry, I meant that we would deal with more than one quadratic

Extracting the terms for this was:

So

and
all equal 0.

Thanks for walking me through this!
Done and dusted,

Linda

#32 Re: Help Me ! » Power Series solution » 2011-09-22 20:53:07

lindah

Hi bobbym,

Thank you for the link! It has some nice Mathematica code

Most of the Frobenius examples (in the link, my text and course notes) usually only deal with indicial equations
where its for e.g.

and so its just quadratic roots

I've been running into incidents where the indicial  would be something along the lines:


Implying:

I am thinking, find the roots of the first equation, meaning
?

#33 Help Me ! » Power Series solution » 2011-09-22 19:38:23

lindah
Replies: 9

Hi guys,

Apologies for the bombardment of DE's eek

70679125.png

I just wanted to see if my setup is correct before continuing, so I hope you can give me feedback smile :

1) This ODE has a regular singular point at x=0, and so Frobenius Method can be applied with

?

2) If the above is correct I have the ODE in series form simplified as:

3) Rewriting them with the common power

I obtain

4) I ask because I am concerned about the next step, as this would mean I would need to take out the first 6 terms of the first 2 series, meaning I would get many indicial roots for (s)

Thank you in advance for any feedback
Linda

#34 Re: Help Me ! » Homogenous Differential Equation » 2011-09-22 12:05:02

lindah

Hi bobbym;

Thank you for that!!!

I will have a try at laying out the generic solution and then your solution.
I'm reading up further on Legendre's solutions

#35 Re: Help Me ! » Homogenous Differential Equation » 2011-09-22 11:17:12

lindah

Hi bobbym;

I outlined that approach in my initial post, but I may think you are on the mark about Legendre polynomials.
I tried k and lambda = 0 and got

Polynomial!!!

#36 Re: Help Me ! » Homogenous Differential Equation » 2011-09-22 11:02:25

lindah

Hi bobbym;

Yes, I am familiar with reduction of order. That would require I know at least one of the solutions?

#37 Re: Help Me ! » Homogenous Differential Equation » 2011-09-22 10:50:00

lindah

Hi bobbym;

Yes, I had a look, it would work well if the coefficients were constants, but since it has

makes it unusual to deal with the roots

I was thinking about using power series to attack this...?

#38 Re: Help Me ! » Homogenous Differential Equation » 2011-09-22 10:07:27

lindah

Hi bobbym;

To be honest I am not sure sad It wasn't explicitly stated by the lecturer
I came across the Chebyshev and Legendre versions after searching the net for similar questions

#39 Help Me ! » Homogenous Differential Equation » 2011-09-22 09:27:47

lindah
Replies: 11

70427339.png

Hi guys,

I am not sure how to approach this question, so would like to ask for hints on approaching this rather than the answer at this point.

In terms of classes, we have not worked with Chebyshev or Legendre polynomials.
It looks like it could be classified as a Euler equation with a solution

for which I then could use reduction of order to find

May I ask if this would be a correct approach?

#40 Re: Help Me ! » Separation of variables: DE » 2011-09-22 02:16:36

lindah
bobbym wrote:

Hi lindah;

You are welcome, I never got around to saying thanks for telling me about the hike you took in Tasmania, I think. You sent me to a page explaining it, I had no idea there were so many rules to be followed.

Hi bobby;

Yes, you did say thanks a while back!
Some parts are World Heritage Listed and there have been lots of cases of people getting lost and injured since some hikes can be catered to being only biking and kayaking, so they are quite stringent with the rules.

Are you a bit of hiker?

#41 Re: Help Me ! » Separation of variables: DE » 2011-09-22 02:08:20

lindah
bobbym wrote:

What happened to the Stochastic Calculus?

Hi bobbym;

I had to reorganize my course progression so that I'm enrolled in 4 subjects per semester.
If I had taken up Stochastic Calculus this semester, I would only have 3 subjects available next semester.
This subject (DE) won't be available until Spring next year, while Stochastic Calculus is available all year around.

I was initially excited to do Stochastic Calculus, but upon looking at some texts, I am slightly glad it won't be until next year big_smile

#42 Re: Help Me ! » Separation of variables: DE » 2011-09-22 01:56:23

lindah

Hi guys,

It makes sense to me when taking logarithms it is the absolute value.

Thank you very much for clearer that up!!! smile
Linda

#43 Re: Help Me ! » Separation of variables: DE » 2011-09-22 01:16:08

lindah

Hi bob and bobbym;

Thank you for the feedback!!!
I will follow up with my lecturer (its an assignment question) since we haven't covered Lambert/Product Logs before, though I can see Mathematica expresses it in that form.

As I need to show working how I obtain my answer, I just tried the integration by hand again and see no opportunity (yet) for it to become (4-2w)

#44 Re: Help Me ! » Separation of variables: DE » 2011-09-22 00:58:31

lindah

Hi bob and bobbym;

When I do the calculations by hand I get (2w-4), but when I run it through Mathematica I get (4-2w)
I am not too sure why the difference sad

Yes the question doesn't seem to ask for that. When I asked my lecturer he was very vague.
In your experiences, have you guys ever had to go further than that answer?

Thank you for taking a look!!!
Linda

#45 Help Me ! » Separation of variables: DE » 2011-09-22 00:33:07

lindah
Replies: 21

29495717.png

Hi guys,
I am having a bit of difficulty obtaining an answer for this, since I suspect the answer will be in implicit form.
May I ask if I have set up the separation of variables correctly?

First I have:


Substituting these into original equation:


From here I integrate both sides but obtain:


I am not sure how to express this in terms of w to obtain the solution to y(x)

Any tips would be greatly appreciated!!!!
tia
Linda

#46 Re: Help Me ! » Two stage least squares » 2011-08-29 19:23:00

lindah

Hi bobbym;

Thanks for the links. The errors-in-variables methods were what I had to address - so finding instrument variables for the independent variable in question
In my case there was no need to account for measurement errors in the dependent variable.

Thanks for posting the links!!

#47 Re: Help Me ! » Two stage least squares » 2011-08-27 23:26:13

lindah

Hi bobbym,

Hope you have a good nap, wish I could have one!!!

The variance of the errors are just assumed to be

, with a mean of 0 - so i.i.d

I appreciate the feedback given!

#48 Re: Help Me ! » Two stage least squares » 2011-08-27 21:07:52

lindah

Hi bobbym;

Actually y = Treasury bill rate and x = inflation rates. For this question we were told to assume errors are normally distributed with E[e] = 0

It's such a weird question!!

#49 Re: Help Me ! » Two stage least squares » 2011-08-27 20:15:34

lindah

Hi bobbym,

What's SNC in this context?

#50 Re: Help Me ! » Two stage least squares » 2011-08-27 19:33:19

lindah

Hi bobbym;

What I thought was any measurement errors were captured in

.

I'll take the excerpt as follows from the question:

Discuss the possibility that the estimated coefficients from the model are inconsistent due to measurement error bias. What strategies are available to reduce such bias?

I also found this:
http://support.sas.com/documentation/cd … ect003.htm

The question was in the context of Instrumental Variables Estimation, so it seems like my lecturer is pushing us to use this to correct for measuring errors.

Or am I confusing everyone in the process even more?

Thanks,
Linda

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