Uni Stuff > Mathematics
Vector Calculus
TrueTears:
--- Quote from: tram on July 28, 2010, 08:48:36 pm ---ran into this question (or a very similar question) in umep....i don't get limits.... like, how do you know how you know which path you should approach the limit from to prove it dosen't exist? and if it's just a proof by contradiction, if the limit DOES exist, how do you prove it exists cos it's not like you can go though every single possibilty it and prove they ALL work.....
is there a thread explaining limits somewhere? soz to be all nooby >.<
--- Quote from: Ilovemathsmeth on July 28, 2010, 06:04:09 pm ---WOW I'd love to do this subject. I don't think Actuarial requires it though :(
--- End quote ---
Vector caculus is the subject they recommend you do in first semester for acturial if you've done umep. Thus it would be highly likely that some acturial studes people have done this subject.
--- End quote ---
what i do is this, check your normal paths, x/y axis, linear lines, parabolas, if those all yield same limit then try an proof to see if the limit is actually what you conjecture. That is as rigorous as it gets.
QuantumJG:
--- Quote from: tram on July 28, 2010, 08:48:36 pm ---ran into this question (or a very similar question) in umep....i don't get limits.... like, how do you know how you know which path you should approach the limit from to prove it dosen't exist? and if it's just a proof by contradiction, if the limit DOES exist, how do you prove it exists cos it's not like you can go though every single possibilty it and prove they ALL work.....
is there a thread explaining limits somewhere? soz to be all nooby >.<
--- Quote from: Ilovemathsmeth on July 28, 2010, 06:04:09 pm ---WOW I'd love to do this subject. I don't think Actuarial requires it though :(
--- End quote ---
Vector caculus is the subject they recommend you do in first semester for acturial if you've done umep. Thus it would be highly likely that some acturial studes people have done this subject.
--- End quote ---
In Vector Calculus we use the sandwhich theorem. Basically you find a function that is always less than your function and one that's greater than your function and you squeeze your function inbetween them and use it to prove the limit exists.
ε-δ proofs I just hate and apparently in vector calculus you aren't required to use them. Although I should probably refresh my memory on them.
tram:
*brain explodes*
ok i'm going and doing some reading on that e-d thingy proof and the sandwich theorem THEN comming back to annoy you guys :)
Mao:
Simple answer to your 'what is a limit', it is a value you get as you approach a particular coordinate in a [possibly multivariable] function. Here, the keyword is 'approach'. You may want to know which way we approach it, and the answer to that is EVERY POSSIBLE DIRECTION. For a limit to exist, you must approach the same value from every direction.
For a univariable function (1D), you can only approach a coordinate from left and right. If you can show they go to the same value, then you are done.
For a multivariable function (2D or higher), you can approach a coordinate from an infinite number of paths, thus you can't use the above method. What we end up employing is the epsilon-delta proof, which incorporates the infinite number of paths. However, it is tedious, algebraically intensive and often very confusing, so we don't always want to do an epsilon-delta proof straight away. Instead, we test a few simple paths, which is much simpler than the e-d proof to try to find a counter-case (thus proving a limit does not exist), and if we cannot find a simple counter-case, we do a e-d proof.
QuantumJG:
Using the matrix chain rule evaluate the derivative of:
f(g[f(x,y)]) at (0,1) where f(x,y) = (x2, 2y, x - y) & g(x,y,z) = (x + z, y2)
I really need help since I'm finding this area hard.
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