About mathematical modelling...

seraphimvc

i m currently doing mathematical modelling I in UCD as an option in my 1st yr science programme.......:rolleyes:

i did my 4th maths modelling class yesterday........and my idea of dropping the module is seriously increasing............

i have no idea wat did the teacher try to teach us as he is keep doing example and different equations r used with very long and complicated solutions come out everytime---i dun get wats the connection between every thing he taught.......i still have no idea wats the 'core' idea of maths modelling.........:( maybe i m just a weirdo with a different way of thinking.....

is there any1 here did the module b4?tell me wat you know about~i 'll be very grateful:;)
or else...i m juz gonna drop the module......:o

David19

Do you have a link to the course content? Mathematical modelling is basically applied maths.

seraphimvc

David19 wrote:

Do you have a link to the course content? Mathematical modelling is basically applied maths.

oic,just realise tat it is some sort of applied maths~
yes,i did applied maths in LC...but we seems didnt cover wats the teacher teaching though:cool:

elivsvonchiaing

Presumably this course has a computer modeling element? In my case I could only make sense of maths through computers - it was an unreal abstract bollox until then...

That said it does depend on your lecturer (not to turn it into a stream of - (we know what we mean!))

Professor_Fink

Nope. If the course is still the same, it is essentially a course on using ODEs and PDEs to model physical systems. There are no computers, that's not what they mean by modeling.

Did he use an example about the change in shark population in the mediteranian during world war 2?

Professor_Fink

That said, it has been 6 years since I did the course.

seraphimvc

Professor_Fink wrote:

Nope. If the course is still the same, it is essentially a course on using ODEs and PDEs to model physical systems. There are no computers, that's not what they mean by modeling.

Did he use an example about the change in shark population in the mediteranian during world war 2?

yup,sort of.;)
population of carp in a lake
i cant believe my eyes when i take a look of the homework.
should i show u guys here?

seraphimvc

tis is the link of the course
https://sisweb.ucd.ie/usis/w_sm_web_inf_browser.show_module?p_subj=MAPH&p_crse=10010&p_term_code=200600&p_crumb=%3CA%20href%3D%22https%3A%2F%2Fsisweb.ucd.ie%2Fusis%2Fw_sm_web_inf_browser.program_list%3F%22%3E%20UCD%20CAO%20Entry%20Routes%3C%2FA%3E%3CA%20href%3D%22https%3A%2F%2Fsisweb.ucd.ie%2Fusis%2Fw_sm_web_inf_browser.show_major%3Fp_term_code%3D200600%26p_major_code%3D576%26p_show_prog_link%3DY%26p_crumb%3D%253CA%2520href%253D%2522https%253A%252F%252Fsisweb.ucd.ie%252Fusis%252Fw_sm_web_inf_browser.program_list%253F%2522%253E%2520UCD%2520CAO%2520Entry%2520Routes%253C%252FA%253E%22%3E%20Mathematical%20Science%3C%2FA%3E

and this is the homework i got.i m pretty impressed that i have no idea what is the difference between linear and nonlinear now.
http://www.savefile.com/files/109301

maybe u guys can give any comment for it.:p

Professor_Fink

Ok, it's pretty simple:

The equation is linear if it is polynomial in the variables, although sometimes this is used to mean 1st order in the arguements (but not in the context of your assignment).

The order is merely the maximum power to which the variable is raised.

Hope this helps. Since it's your homework, I won't give you the answers, but if you need clarification on any points, feel free to ask.

seraphimvc

Professor_Fink wrote:

Ok, it's pretty simple:

The equation is linear if it is polynomial in the variables, although sometimes this is used to mean 1st order in the arguements (but not in the context of your assignment).

The order is merely the maximum power to which the variable is raised.

Hope this helps. Since it's your homework, I won't give you the answers, but if you need clarification on any points, feel free to ask.

thank you so much of willing to help:D i found that those questions are actually quite 'basic' today,but they become a problem when the teacher didnt really teach us about them.
i sort out most parts in question 1.to get the power,just subtract the highest power by the lowest power,right?i just dont really sure which 1 of them is linear or nonlinear,my answer is a=linear,b=nonlinear,c=nonlinear,is it right?i still dont get the concept of the linear and nonlinear.we learned that something like ax+by=0,this sort of equation is linear ,but the equations in Q.1 are just different.....:rolleyes:
i sort out question 3 and 4 as well.i m just not sure again wat should i write for Q.3 to get a full marks.
i have no idea about Q.2 and trying to do Q.5 now.maybe you can give an example by doing the part (a) in Q.2 for me?:p

Professor_Fink

seraphimvc wrote:

thank you so much of willing to help:D i found that those questions are actually quite 'basic' today,but they become a problem when the teacher didnt really teach us about them.

You'll find that lecturers don't teach you in the same way teachers do in school. They WILL ask questions which they haven't told you how to answer. You're supposed to be able to figure out how to do it by reading up on the subject. Usually they don't even recommend any one book, since your supposed to read around a subject (several sources for any one topic).

seraphimvc wrote:

i sort out most parts in question 1.to get the power,just subtract the highest power by the lowest power,right?

Well, they're not powers, and no, not exactly. It's just the number of different variables in this case. (My original post on this contains an error because I misinterpreted what you were asking)

seraphimvc wrote:

i just dont really sure which 1 of them is linear or nonlinear,my answer is a=linear,b=nonlinear,c=nonlinear,is it right?i still dont get the concept of the linear and nonlinear.we learned that something like ax+by=0,this sort of equation is linear ,but the equations in Q.1 are just different.....:rolleyes:

Ok, any question that contains trigonometric functions (sin,cos,sinh, cosh etc.) or exponentials (e^x) along with polynomials (x, x^2, etc.) is non-linear. If it just has polynomials then it is linear.

What I mean here is functions of x_n etc, not functions of constants.

C is linear.

seraphimvc wrote:

i sort out question 3 and 4 as well.i m just not sure again wat should i write for Q.3 to get a full marks.
i have no idea about Q.2 and trying to do Q.5 now.maybe you can give an example by doing the part (a) in Q.2 for me?:p

Ok, in question 2 they are just asking you to calculate x_n explicitly, rather than as a recursion relation.

In 2(a) x_n - 2x_{n-1}= 0, so x_n = 2 x_{n-1} = 2^2 x_{n-2} = ... = 2^n x_{n-n} = 2^n x_0

So 2^n x_0 is your answer.

seraphimvc

Professor_Fink wrote:

You'll find that lecturers don't teach you in the same way teachers do in school. They WILL ask questions which they haven't told you how to answer. You're supposed to be able to figure out how to do it by reading up on the subject. Usually they don't even recommend any one book, since your supposed to read around a subject (several sources for any one topic).

yah,i think so.but i have run through the library to get a book which may show me some examples...eventually i failed...maybe this kinad stuff is too basic...:o

Professor_Fink wrote:

Well, they're not powers, and no, not exactly. It's just the number of different variables in this case. (My original post on this contains an error because I misinterpreted what you were asking)

opps....my bad;) i never really learn off all those nouns off by heart.i think i should do tat from now on.

Professor_Fink wrote:

Ok, any question that contains trigonometric functions (sin,cos,sinh, cosh etc.) or exponentials (e^x) along with polynomials (x, x^2, etc.) is non-linear. If it just has polynomials then it is linear.

oh my god,this completely clear up my mind!!!thanks a million!

Professor_Fink wrote:

Ok, in question 2 they are just asking you to calculate x_n explicitly, rather than as a recursion relation.

In 2(a) x_n - 2x_{n-1}= 0, so x_n = 2 x_{n-1} = 2^2 x_{n-2} = ... = 2^n x_{n-n} = 2^n x_0

So 2^n x_0 is your answer.

why is tat 2 x_{n-1} = 2^2 x_{n-2}???:eek:
i think tats the core concept of the whole thing....
wat is the relations between x_n , x_{n-1} ,x_{n-2}anyway.i knew tat they mean one hour later(or earlier)in Q.4,but this 1?

Professor_Fink

There is a possibility I've completely messed up my answer about the order of equations. Best to check with someone else.

As for answering Q2:
You have x_n - 2 x_{n-1} = 0, so rearranging this we get x_n = 2 x_{n-1}.

But this is true for any n, so x_k=2 x_{k-1} and x_{k-1} = 2 x_{k-2} etc.

Substituting the second equation into the first, you get x_k = 2 (2 x_{k-2}) =2^2 x_{k-2}.

So x_k = 2^m x_{k-m} = 2^n x_0. Now rename k to n, and you get x_n = 2^n x_0

seraphimvc

Professor_Fink wrote:

There is a possibility I've completely messed up my answer about the order of equations. Best to check with someone else.

As for answering Q2:
You have x_n - 2 x_{n-1} = 0, so rearranging this we get x_n = 2 x_{n-1}.

But this is true for any n, so x_k=2 x_{k-1} and x_{k-1} = 2 x_{k-2} etc.

Substituting the second equation into the first, you get x_k = 2 (2 x_{k-2}) =2^2 x_{k-2}.

So x_k = 2^m x_{k-m} = 2^n x_0. Now rename k to n, and you get x_n = 2^n x_0

oh i see:D i think i m fine now:D seriously thanks alot!!!

about the Q.1,i m sure i got it right in the power part
take the highest variables subtract lowest variables,u get the order.(e.g:part (a) in question 1 :n+2-n+1=3,power is 3);)

professor fink?r u still a student?:p i guess you already graduate from college,right?doing postgraduate?or really a professor?:D

Professor_Fink

Professor Fink is a Simpsons character. I'm just finishing my doctorate in Oxford. I graduated from UCD in theoretical physics in 2004.

Oh, and you may well be write about the order. I haven't really come across it used in that context before.

seraphimvc

Professor_Fink wrote:

Professor Fink is a Simpsons character. I'm just finishing my doctorate in Oxford. I graduated from UCD in theoretical physics in 2004.

Oh, and you may well be write about the order. I haven't really come across it used in that context before.

:eek: cool!!i have heard that theoretical physics is like one of the hardest course on earth!!:eek: wat r u planning to do after that??

i spent my whole afternoon to try to finish the paper.i give up just now.so i online to seek for help again:(

Q2 part b/c is totally from part a ,is it? show me how to do part b,maybe?or just giving me some tips....:o

i have no idea how to solve Q5 as well.......poor me....:o i think i still dont understand the core concept.....lol

Professor_Fink

Ok,

2b) Yu have an expression for x_n in terms of x_{n-1}:

x_n = x_{n-1} + 3. Just as before, this holds for all n, so x_{n-1} = x_{n-2} + 3.

Sub this into the first, and you get x_n = (x_{n-2} + 3)+3. So x_n = x_{n-m} + 3*m.

So your answer is x_n = x_0 + 3n. Part c is similar, but you should try it again your self before I give you the answer.

For Q5 use the geometric-arithmetic series solution they give you in 2. It's more or less the same as 2.

seraphimvc

Professor_Fink wrote:

Ok,

2b) Yu have an expression for x_n in terms of x_{n-1}:

x_n = x_{n-1} + 3. Just as before, this holds for all n, so x_{n-1} = x_{n-2} + 3.

Sub this into the first, and you get x_n = (x_{n-2} + 3)+3. So x_n = x_{n-m} + 3*m.

So your answer is x_n = x_0 + 3n. Part c is similar, but you should try it again your self before I give you the answer.

For Q5 use the geometric-arithmetic series solution they give you in 2. It's more or less the same as 2.

i m impressed again.we can play the equation in this ways~:p :eek:

i m too happy to get to know the answer which makes my hands keep trembling makes me take longer to solve the part c.i got X_n = X_0 + n/2,is tat right?
i plus 1 for the equation this time.

p/s:seriously thanks again.

Professor_Fink

If you want me to talk you through the questions, we can do it over IM if you have AOL instant messenger/MSN messenge/Yahoo if you have any of them. If you want to, just let me know.

seraphimvc

Professor_Fink wrote:

If you want me to talk you through the questions, we can do it over IM if you have AOL instant messenger/MSN messenge/Yahoo if you have any of them. If you want to, just let me know.

yeh,sure:)

Pm you my Msn messenger email address.

Professor_Fink

You're very close on part c:

2c) x_n + x_{n-1} = n, so x_n = n - x_{n-1}

x_{n-1} = n-1 - x_{n-2}

So x_n = 1 + x{n-2}

-> x_2n = 1 + x_2(n-1) -> x_2n = n + x_0

x_{2n+1} = 1 + x_{2(n-1) - 1} -> x_{2n-1} = n + x_1 = n + 1 - x_0

So you have slightly different results for even and odd terms. You have to be careful with those.

seraphimvc

Professor_Fink wrote:

You're very close on part c:
x_{n-1} = n-1 - x_{n-2}

So x_n = 1 + x{n-2}

sorry,wats going on here??

ah,i get it now~

von Bismarck

hey classmate!!

mathematical modeeling 1 is easily the best class i'm doing ... the most interesting anyway.

just look up the notes on blackboard and if you don't follow anything, ask dr. cox, he'll help you out anytime.