What's the deal witih Calculus?

[philecon]

Originally Posted by rcwlhk

Here's my two cents on this whole calculus gig (disclaimer: I'm not in econ grad school yet). Let's face it --- of all the math courses that we do in undergrad and beyond, you need to be able to "think" mathematically. That is, at the very least, you shouldn't be afraid of math symbols and equations. Calculus does provide this foundation very well. So, if an applicant / student can't even do Calculus (again, "cook book" style Calculus), it makes you wonder how well can he fair in other more advanced courses.

I'm not in grad echool either, but I would agree with this statement. I was talking to a professor in our school's math department, and she told that even if upper division math is way different compared to "cook-book" calculus, the entire series helps in developing your mathematical maturity. (Like, in my school, we were introduced to epsilon-delta proofs in Calc I, but then again, my calc series is different from the calc series of engineering majors). Plus, you get introduced to important results that you will see again when you take analysis (i.e., Mean Value Theorem).

[andrem]

Yes!!

Originally Posted by cooper

Surely you mean physicists not physicians unless he is having conversations about the human body as a complex system--no pun intended .

As far as computational calculus, meaning computing derivatives, integrals, etc, integration by parts pops up in auctions (allthough this is really calc 2) and I remember seeing this other places too but can not remember. As others have mentioned, in macro, multivariable differentiation should be second nature. Allthough its not necessary to get through first semester Micro (using Mas-Collel et. al.) you should understand gradients to build intuition when utility functions are differentiable.

[rcwlhk]

Hmm.... so let me get this straight.

Can somebody provide a YES / NO / MAYBE to the following questions regarding topics and concepts in Calculus? (Disclaimer --- I have studied / will be studying these topics and I do enjoy them. But I just want some clarifications on their applications in economics).

(i) Any use of polar, cylindrical, spherical coordinates? (I can surmise NO, but just want to make sure).

(ii) Even for the calculation of double or triple integrals, would we be considering the region D that is non-rectangular / non-cubic? (i.e. region D is not the set D = {(x, y) : a <= x <= b, c <= y <= d } ? ). I ask this because it was literally living hell to think about how to compute complicated and non-rectangular region D's.

(iii) Any use of parametrized representations of planes and surfaces? And their associated surface integrals? Vector fields? What about curl and divergence?

(iv) OK, the gradient vector is useful --- but it isn't exactly a very profound idea either (i.e. the direction of the gradient is the direction of greatest ascent / increase).

I still can't really wrap my head around why you would seriously need anything more than Calc I to II + a bit more if most of the concepts in Calc III - IV are not even used at all in economic applications!

[treblekicker]

Multivariable Calc topics (specifically higher order integrals) come up quite a bit in probability and math stats which are obviously very relevant to economics.

In fact I remember a pretty hard math stats problem where we had to calculate the power of a test and it had a lot to do with correctly identifying the region over which you are integrating.

[treblekicker]

Originally Posted by rcwlhk

Hmm.... so let me get this straight.

Can somebody provide a YES / NO / MAYBE to the following questions regarding topics and concepts in Calculus? (Disclaimer --- I have studied / will be studying these topics and I do enjoy them. But I just want some clarifications on their applications in economics).

(i) Any use of polar, cylindrical, spherical coordinates? (I can surmise NO, but just want to make sure).

(ii) Even for the calculation of double or triple integrals, would we be considering the region D that is non-rectangular / non-cubic? (i.e. region D is not the set D = {(x, y) : a <= x <= b, c <= y <= d } ? ). I ask this because it was literally living hell to think about how to compute complicated and non-rectangular region D's.

(iii) Any use of parametrized representations of planes and surfaces? And their associated surface integrals? Vector fields? What about curl and divergence?

(iv) OK, the gradient vector is useful --- but it isn't exactly a very profound idea either (i.e. the direction of the gradient is the direction of greatest ascent / increase).

I still can't really wrap my head around why you would seriously need anything more than Calc I to II + a bit more if most of the concepts in Calc III - IV are not even used at all in economic applications!

Also I would like to mention if you take a PDE course, a lot of Calc III topics are used frequently, especially changing to spherical and cylindrical coordinates. So if you are interested in finance, most of this stuff will be useful.

[Thesus]

Originally Posted by rcwlhk

Hmm.... so let me get this straight.

Can somebody provide a YES / NO / MAYBE to the following questions regarding topics and concepts in Calculus? (Disclaimer --- I have studied / will be studying these topics and I do enjoy them. But I just want some clarifications on their applications in economics).

(ii) Even for the calculation of double or triple integrals, would we be considering the region D that is non-rectangular / non-cubic? (i.e. region D is not the set D = {(x, y) : a <= x <= b, c <= y <= d } ? ). I ask this because it was literally living hell to think about how to compute complicated and non-rectangular region D's.

This one came up a zillion times in the proof-based probability sequence I did, so maybe it shows up in metrics?