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Think Differently

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Re: Think Differently

#21

Post by nostrademons »

cperciva wrote: post #5

I had a similar experience as an undergraduate, except that I didn't get the marks: I was taking a course on differential equations, and one of the final exam questions was to demonstrate that a solution existed to a given system. I gave a very elegant non-constructive proof which showed that a solution existed without giving any hint of what the solution was -- but the instructor expected students to provide a solut…

I had a similar experience when taking functions of a complex variable, where a midterm problem asked you to show that a solution existed and several students (not me, alas) found a non-constructive proof that worked without actually finding a solution. Unlike in your case, though, the professor gave all of them full credit.

I had good math professors. Too bad I wasn't a good math student.

Re: Think Differently

#24

Post by andreyf »

cperciva wrote: post #5

I had a similar experience as an undergraduate, except that I didn't get the marks: I was taking a course on differential equations, and one of the final exam questions was to demonstrate that a solution existed to a given system. I gave a very elegant non-constructive proof which showed that a solution existed without giving any hint of what the solution was -- but the instructor expected students to provide a solut…

it wasn't worth the effort of formally appealing the grade

If the question actually asked to demonstrate that a solution existed, any professor worth her salt will give you credit for doing that if you point it out to her. It's quite possible you weren't given full marks because your exam was one of hundreds that needed to be graded that week.

Re: Think Differently

#25

Post by gur »

sant0sk1 wrote: post #4
hhm wrote: post #3

Nope: http://www.snopes.com/college/exam/barometer.asp

This story maintains its value whether fact or fiction.

As italians say, "se non è vero, è ben trovato". ("Even if it is not true, it is well conceived")

Re: Think Differently

#26

Post by pkrumins »

Here is how I would do the puzzle about barometer:

PV = nRT; n = m/M

PV = mRT/M; V = m/(rho)

p*m/(rho) = mRT/M

p/(rho) = RT/M

(rho) = pM/RT

p + (dp) = p + (rho)g(dh)

(dp) = (rho)g(dh)

(dp) = pMg(dh)/RT

(dp)/p = Mg(dh)/RT

integrate 0 to p (dp)/p = integrate h to 0 [Mg(dh)/RT]

ln(p) = -Mgh/RT + c

take h = 0 at bottom of building, then

ln(p_at_h=0) = c => read c from barometer to get constant

now, at height h we will read p_at_h=height from barometer, then:

ln(p_at_h=height) = -Mgh/RT + ln(p_at_h=0)

Mgh/RT = -ln(p_at_h=height) + ln(p_at_h=0)

Mgh = -RTln(p_at_h=height) + RTln(p_at_h=0)

-----------------------------------------------------------------------------

| height = -RTln(p_at_h=height)/Mg + RTln(p_at_h=0)/Mg =

| = RT/Mg(ln(p_at_h=0) - ln(p_at_h=height)) =

| = RT/Mg(ln(p_at_h=0/p_at_h=height))

-----------------------------------------------------------------------------

p in Pascals

g = 9.81

R = 8.31

T = temperature in absolute units

M = 28.97

I hope i did it right ;)

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