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October 19, 2025, 01:49:57 am
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Author Topic: Vector Calculus  (Read 8237 times)  Share 

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Ilovemathsmeth

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Re: Vector Calculus
« Reply #15 on: September 10, 2010, 12:23:08 am »
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tram - does that mean you can possibly choose it as a breadth subject? They said 'no-maths' though...
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tram

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Re: Vector Calculus
« Reply #16 on: September 10, 2010, 09:34:47 pm »
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Well yeah, i think the rule is bcs you're already 'using up' breath subjects in maths you can't choose any more maths as breath. Plus the point of breath is to do subjects DIFFERENT to what youa re doing in ur main cosue which is obvs very math heavy for act stud.
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Ilovemathsmeth

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Re: Vector Calculus
« Reply #17 on: September 19, 2010, 12:59:03 am »
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ahh no that sucks, got to find a breadth sub for next yr lol.
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QuantumJG

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Re: Vector Calculus
« Reply #18 on: September 30, 2010, 08:42:41 pm »
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I don't know where to start with solving this question.

BTW: The answer is 1/2.
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/0

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Re: Vector Calculus
« Reply #19 on: September 30, 2010, 09:07:57 pm »
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The Jacobian is

So we have:



In order to find the limits of integration for the region D',

The region , is the triangle with sides , , .

The side transforms to in the u-v plane.
The side transforms to .
The side transforms to .
The region of integration is the enclosed triangle

If you graph this you will see you must integrate

« Last Edit: September 30, 2010, 09:11:10 pm by /0 »
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AzureBlue

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Re: Vector Calculus
« Reply #20 on: September 30, 2010, 09:14:43 pm »
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Quote from: tram on September 10, 2010, 09:34:47 pm
Well yeah, i think the rule is bcs you're already 'using up' breath subjects in maths you can't choose any more maths as breath. Plus the point of breath is to do subjects DIFFERENT to what youa re doing in ur main cosue which is obvs very math heavy for act stud.
The breadth subjects for actuarial studies are not finalised yet - thus, they might end up being electives/breadth/or non-maths breadth. Better to wait until subject selection next year. But yes, vector calculus is used as breadth in maths. I love the economics plan actually - so many comm electives and breadth! ahhhh... :) If I end up doing Eco, I'll still probably accelerate vector calculus to breadth in first-year for the DipMSc.
« Last Edit: September 30, 2010, 09:16:25 pm by AzureBlue »
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QuantumJG

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Re: Vector Calculus
« Reply #21 on: October 02, 2010, 01:54:26 pm »
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Ok I'm stuck on this:

Find the moment of inertia about the y-axis of a ball defined by x^2 + y^2 + z^2 R^2 where the mass density ρ is a constant.

My problem is the x^2 + z^2 part in the integral. In spherical coordinates (what I want to use) it doesn't simplify.
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kamil9876

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Re: Vector Calculus
« Reply #22 on: October 02, 2010, 02:18:01 pm »
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Post the rest of what you have done so far, and we will see what we can do. Cbf doing everything from scratch.
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QuantumJG

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Re: Vector Calculus
« Reply #23 on: October 02, 2010, 03:52:10 pm »
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Well I have the limits of integration ( 0 < r < R, 0 < θ < π, 0 < φ < 2π ).

But it's the ugly bit inside that's annoying me! Does r2sinθ*(x2 + z2) simplify to something nice?
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AzureBlue

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Re: Vector Calculus
« Reply #24 on: October 02, 2010, 03:54:13 pm »
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Quote from: Ilovemathsmeth on September 19, 2010, 12:59:03 am
ahh no that sucks, got to find a breadth sub for next yr lol.
Considering you have Principles of Business Law this year, probably choose Corporate Law next year as breadth maybe because you will have met the pre-reqs.
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kamil9876

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Re: Vector Calculus
« Reply #25 on: October 02, 2010, 06:38:49 pm »
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Quote from: QuantumJG on October 02, 2010, 03:52:10 pm
Well I have the limits of integration ( 0 < r < R, 0 < θ < π, 0 < φ < 2π ).

But it's the ugly bit inside that's annoying me! Does r2sinθ*(x2 + z2) simplify to something nice?

Actually maybe try to use cylindrical co-ordinates, that way that bit is just merely

Tho with what you have now, you have to find something to change to something nice using trigonometry. or . I forgot which letter corresponds to which angle.
« Last Edit: October 02, 2010, 06:44:47 pm by kamil9876 »
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TrueTears

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Re: Vector Calculus
« Reply #26 on: October 02, 2010, 10:03:01 pm »
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phi for angle made with z axis.

theta for angle made with positive x axis.
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Ilovemathsmeth

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Re: Vector Calculus
« Reply #27 on: October 10, 2010, 01:53:06 am »
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thanks for the advice azureblue :)

i dunno about corporate law, pbl kinda scarred me for life... haha
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/0

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Re: Vector Calculus
« Reply #28 on: October 10, 2010, 03:29:32 pm »
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Quote from: TrueTears on October 02, 2010, 10:03:01 pm
phi for angle made with z axis.

theta for angle made with positive x axis.

That's the way I always used to do spherical, until I read Griffiths electrodynamics. Now I use for angles with the x-axis in cylind and spher, unless it's only 2D in which case I use . Makes no sense, but whatever... when in Rome
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TrueTears

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Re: Vector Calculus
« Reply #29 on: October 10, 2010, 04:59:03 pm »
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Lol yeah hate it when conventional gets changed ><
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