Double integration using polar coordinates

Click For Summary

Discussion Overview

The discussion revolves around the challenges of double integration using polar coordinates, particularly focusing on determining the limits for theta in various scenarios. Participants express their difficulties with applying the beta function and understanding the geometric interpretation of polar coordinates.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested, Homework-related

Main Points Raised

  • One participant expresses confusion about determining the limits for theta beyond the first quadrant, indicating a lack of understanding of how to apply the beta function in different contexts.
  • Another participant suggests that memorizing formulas is not effective and encourages visualizing the mapping of polar coordinates to the Cartesian plane to understand the limits better.
  • A third participant seeks clarification on the previous comment, indicating a focus on memorization for exam purposes rather than deeper understanding.
  • Another reply emphasizes the importance of drawing diagrams to comprehend the bounds of integration, arguing that memorization alone is insufficient and that critical thinking should be maintained regardless of future math studies.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to understanding the limits for theta. There are competing views on the effectiveness of memorization versus conceptual understanding through visualization.

Contextual Notes

Participants acknowledge that the first quadrant limit of pi/2 may not always apply, suggesting that specific problems may require different considerations. There is an indication of missing assumptions regarding the geometric interpretation of polar coordinates.

Who May Find This Useful

Students preparing for exams in mathematics or related fields, particularly those struggling with polar coordinates and integration techniques.

tigrisdea
Messages
2
Reaction score
0
Ok, got a few small problems. Just gaps in my knowledge I suppose, wonder if anyone can help.

A bit stuck on how to work out the limits for theta. Everything else is fine, it's just that. I know if it says in the first quadrant that it's pi/2 and 0 but that's a really basic one, everything above that, no clue.

Beta function formula for anything that isn't from 0 to pi/2 :( I don't understand what number you multiply it by. Normal beta function is fine, just that.

Think that's it for now. Help would be greatly appreciated :)
 
Physics news on Phys.org
it sounds like you are trying to memorize a formula for every situation, always useless.

try picturing what the polkar coord map does to a rectangle 0 < r < A, 0 < theta < B, when mapping it to the x,y plane by sending (r,theta) to (rcostheta, rsintheta).
 
Uh, I'm not sure what you mean. Could you be a bit more explicit? Just so you know, I'm not taking maths any further, so I am really just trying to memorise things so I can pass the exam
 
I think what mathwonk is saying is that you should draw a picture of what is happening and realize where the bounds occur. Simply memorizing situations will illy prepare you for anything. There is not really a set pattern you follow to find the bounds, even your first quadran = pi/2 can be wrong if given the right problem.

Even if you do not plan to take more mathematics, you shouldn't plan to stop thinking critically.
 

Similar threads

MHB Double Integrals in Polar Coordinates
  • · Replies 4 ·
Replies
4
Views
2K
MHB Iterated Integral in Polar Coordinates
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Centre of mass of a semicircle using polar coordinates
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad Double Integrals in Polar Coordinates
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Simple dot product in polar coordinates
  • · Replies 20 ·
Replies
20
Views
7K
MHB Double Integrals in Polar Coordinates
  • · Replies 6 ·
Replies
6
Views
3K
MHB Polar coordinates to evaluate double integral
  • · Replies 1 ·
Replies
1
Views
2K
MHB Calculating integral using polar coordinates
  • · Replies 5 ·
Replies
5
Views
2K
Double Integral of function in region bounded by two circles
  • · Replies 19 ·
Replies
19
Views
3K
Undergrad Gaussian Integral Coordinate Change
  • · Replies 4 ·
Replies
4
Views
2K