You are Here: Home >< Maths

Projection of surface differential onto xy plane. watch

1. Reading a book on surface integrals I ran into the following formula.

Which seems to be quite handy for evaluating surfaces integrals rather than bringing out partial derivatives and cross products.

I can't seem to see exactly where this comes from though.

I mean intuitively it seems to make some sense that ds would depend on dxdy and then the angle between n and k but I don't see exactly why it would look like this in particular.

Anyone can explain?

I tried to look online for a sketch as I guess that would clear it up but couldn't see anything.

thanks.
2. (Original post by poorform)
Reading a book on surface integrals I ran into the following formula.

Which seems to be quite handy for evaluating surfaces integrals rather than bringing out partial derivatives and cross products.

I can't seem to see exactly where this comes from though.

I mean intuitively it seems to make some sense that ds would depend on dxdy and then the angle between n and k but I don't see exactly why it would look like this in particular.

Anyone can explain?

I tried to look online for a sketch as I guess that would clear it up but couldn't see anything.

thanks.
it is a geometric proof involving the angle between the normal and the k vector.

it is not long but not easy to explain

Look for a "glossy type American book on Calculus" although some books use an alternative formula (the one with the square root). They tend to have very good diagrams and their explanations are for "dummies"
3. (Original post by TeeEm)
it is a geometric proof involving the angle between the normal and the k vector.

it is not long but not easy to explain

Look for a "glossy type American book on Calculus" although some books use an alternative formula (the one with the square root). They tend to have very good diagrams and their explanations are for "dummies"
You referring to the one?

And will do thanks.
4. (Original post by poorform)
You referring to the one?

And will do thanks.
yes this is the formula (sorry NO LaTeX for me)

I rarely use it although it is widely used.
As I said look for a "CALCULUS WITH ANALYTIC GEOMETRY" type book in your University library.

Otherwise if you have no luck I will dig it up
5. This might help:

http://onlinelibrary.wiley.com/doi/1...37711.app1/pdf
6. Got it thanks. Managed to dig this up on an e-book after searching.
7. (Original post by poorform)
Got it thanks. Managed to dig this up on an e-book after searching.
all good
8. (Original post by poorform)
Got it thanks. Managed to dig this up on an e-book after searching.
To my mind this is still just "stating" the important bit ("the projection of dS on the xy plane is "), but if that works for you don't worry about it!

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 2, 2015
Today on TSR

Discuss upcoming interviews...

University open days

• Heriot-Watt University
School of Textiles and Design Undergraduate
Fri, 16 Nov '18
• University of Roehampton
Sat, 17 Nov '18
• Edge Hill University
Faculty of Health and Social Care Undergraduate
Sat, 17 Nov '18
Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants