martini Posted February 8, 2010 Share Posted February 8, 2010 It's been a good five years since I did any differentiation, so I wondered if someone could help me with a relatively easy equation... I need to differentiate this with respect to RHm: Gc=(1+(gm^3-1)((1-RHm)RHt)/(1-RHt)RHm)^1/3 It's probably much easier to read here: http://img.skitch.com/20100208-gr6mrqj9uygh81bitbc2xn7dqe.jpg Help on this would be greatly appreciated Link to comment Share on other sites More sharing options...
marc_p Posted February 8, 2010 Share Posted February 8, 2010 It's been a good five years since I did any differentiation You lost me there.... Link to comment Share on other sites More sharing options...
Abz Posted February 8, 2010 Share Posted February 8, 2010 I know we have some clever people on here but only a scientist would be able to work that one out. Oh... You are a scientist Link to comment Share on other sites More sharing options...
stevie_b Posted February 8, 2010 Share Posted February 8, 2010 I'm rusty too but... the first question is, are RHt and gm constants w.r.t. RHm? Link to comment Share on other sites More sharing options...
caseys Posted February 8, 2010 Share Posted February 8, 2010 You should change the equation really and change some of the variables with single letters to help you engineer that. if y = Gcorr, a=Gmeas, x=RHmeas, b=RHtarget then you've got y=(1+(a^3-1) (b/1-b)(1-x/x))^1/3 if you're holding a and b as constant you're looking to diff dy/dx then so it's simple differentiation u=1+(a^3-1)(b/1-b)(1-x/x) to get du/dx = -(a^3-1)(b/1-b)(1/x^2) and so y=u^(1/3) you can work out dy/dx and then mutiply them together. Sorry doing this without being able to draw it out... and haven't done diff since my a-level maths which is criky... about 10 years ago? Link to comment Share on other sites More sharing options...
martini Posted February 8, 2010 Author Share Posted February 8, 2010 I know we have some clever people on here but only a scientist would be able to work that one out. Oh... You are a scientist Cheeky! We need a mathematician, not an atmospheric physicist! I'm rusty too but... the first question is, are RHt and gm constants w.r.t. RHm? After a little thinking about this, I managed to do it. I must have been between 5 and 8 years since I did anything like this... it's been a good reminder! You should change the equation really and change some of the variables with single letters to help you engineer that. if y = Gcorr, a=Gmeas, x=RHmeas, b=RHtarget then you've got y=(1+(a^3-1) (b/1-b)(1-x/x))^1/3 if you're holding a and b as constant you're looking to diff dy/dx then so it's simple differentiation u=1+(a^3-1)(b/1-b)(1-x/x) to get du/dx = -(a^3-1)(b/1-b)(1/x^2) and so y=u^(1/3) you can work out dy/dx and then mutiply them together. Sorry doing this without being able to draw it out... and haven't done diff since my a-level maths which is criky... about 10 years ago? I went away and thought about it for a while, and got the same result as you Similar to Newton and Leibniz? ha! OK, I've managed it and put it into code. Thanks for the input guys (especially caseys ) a=gfavg//GFmeas b=awtarget//Target RH h=awmeas//Measured RH c=((a^3)-1)*(b/(1-b)) dGdRH=-(1/3)*((1+c*((1/h)-1))^(-2/3))*(c/(h^2)) Link to comment Share on other sites More sharing options...
Pixelfill Posted February 8, 2010 Share Posted February 8, 2010 wtf ! I used to understand all this stuff, but it's been 17 years since I last did any differentiation ! scary times. /runs off to wikipedia for a refresher. Mike Link to comment Share on other sites More sharing options...
caseys Posted February 8, 2010 Share Posted February 8, 2010 Cheeky! We need a mathematician, not an atmospheric physicist! After a little thinking about this, I managed to do it. I must have been between 5 and 8 years since I did anything like this... it's been a good reminder! I went away and thought about it for a while, and got the same result as you Similar to Newton and Leibniz? ha! OK, I've managed it and put it into code. Thanks for the input guys (especially caseys ) a=gfavg//GFmeas b=awtarget//Target RH h=awmeas//Measured RH c=((a^3)-1)*(b/(1-b)) dGdRH=-(1/3)*((1+c*((1/h)-1))^(-2/3))*(c/(h^2)) Phew, I wondered if I was fully accurate though, as jet lagged and calculus is not my strong point (I love mechanical/physics maths a lot more). I mean ask me about orbital mechanics or such and you've got me interested Just out of curiosity what's this for? I assume something academic? What you studying? Also I have failed to find the significance of 18571... bar it being a largish prime. It's not a 'weird number' is it?? Link to comment Share on other sites More sharing options...
Gaz6002 Posted February 8, 2010 Share Posted February 8, 2010 I can't even remember where to begin with differentiation. 8 years for me since double maths A level, but my memory has taken quite the battering in those 8 years. Link to comment Share on other sites More sharing options...
Rob_Mitchell Posted February 8, 2010 Share Posted February 8, 2010 WTF im off to the pub for a pint, mccoys and a yorkie bar Link to comment Share on other sites More sharing options...
Pixelfill Posted February 8, 2010 Share Posted February 8, 2010 quick refresher and it's coming back. x^n => nx^(n-1) Chain Rule, product rule - I'm remembering stuff () Mike Link to comment Share on other sites More sharing options...
martini Posted February 8, 2010 Author Share Posted February 8, 2010 Phew, I wondered if I was fully accurate though, as jet lagged and calculus is not my strong point (I love mechanical/physics maths a lot more). I mean ask me about orbital mechanics or such and you've got me interested Just out of curiosity what's this for? I assume something academic? What you studying? Also I have failed to find the significance of 18571... bar it being a largish prime. It's not a 'weird number' is it?? I too prefer orbital mechanics. Especially trying to calculate gravitational forces between 3 bodies This is in an attempt to try and attribute error bars to some measurements I've made in the field. I'm doing a Ph.D in atmospheric physics, and I have taken measurements of particle water uptake from multiple field sites. At this time, there is a lot of published material on how this may change cloud behaviour and so on, but nobody has actually tried propagating measurement errors through into global models (for these instruments). Thus, for my first paper (that I'm currently writing - I'll show you all when it's submitted! ) I want to try to propagate these errors in a kosher manner. This is the code I've written this afternoon for a snippet of what I've been up to: http://img.skitch.com/20100208-kjcm2wya5reag6s4wsw9nqm3q6.jpg As I said, when I finally get my first paper published, I'll show you lot quick refresher and it's coming back. x^n => nx^(n-1) Chain Rule, product rule - I'm remembering stuff () Mike That's it mate! Also I have failed to find the significance of 18571... bar it being a largish prime. It's not a 'weird number' is it?? Nothing fun unfortunately, I'll make the next sig more interesting! Link to comment Share on other sites More sharing options...
supra_aero Posted February 8, 2010 Share Posted February 8, 2010 V. impressive martini. I do hope they pay you for all this malark Link to comment Share on other sites More sharing options...
martini Posted February 8, 2010 Author Share Posted February 8, 2010 V. impressive martini. I do hope they pay you for all this malark Funny you should say that; Government's cut funding for all research departments and I'll be out on money starting next month... will write up the thesis and then I'll be hunting for a real job! Link to comment Share on other sites More sharing options...
supra_aero Posted February 8, 2010 Share Posted February 8, 2010 That's unfortunate. I work in research too ironically. I wish you luck in finding a well paid occupation Link to comment Share on other sites More sharing options...
martini Posted February 8, 2010 Author Share Posted February 8, 2010 That's unfortunate. I work in research too ironically. I wish you luck in finding a well paid occupation Thanks pal What's your area of research? I'm hoping I can land myself a nicely paid job and import a TT someday... Link to comment Share on other sites More sharing options...
Mike Posted February 8, 2010 Share Posted February 8, 2010 errr... just for the record kids it's actually Calculus Yep, I'm in the short term memory loss club too... I did Maths or the first year of my Psychology degree... and then promptly dumped it in Year 2 Link to comment Share on other sites More sharing options...
caseys Posted February 8, 2010 Share Posted February 8, 2010 Phew, I wondered if I was fully accurate though, as jet lagged and calculus is not my strong point (I love mechanical/physics maths a lot more). errr... just for the record kids it's actually Calculus Yep, I'm in the short term memory loss club too... I did Maths or the first year of my Psychology degree... and then promptly dumped it in Year 2 Ahem Notice you took part in the Psychometrics, but is it in fact any good or a load of old tosh? http://www.mkivsupra.net/vbb/showthread.php?t=158016 Link to comment Share on other sites More sharing options...
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