- #1

LinearAlgebra

- 22

- 0

Confused. :shy:

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter LinearAlgebra
- Start date

- #1

LinearAlgebra

- 22

- 0

Confused. :shy:

- #2

arunma

- 927

- 4

Confused. :shy:

You sound like you might be asking what the physical interpretations of these various line integrals are. The last one, G(x,y)ds, is called

There isn't any obvious physical description of the line integrals of G(x,y) with respect to x or y (not one that I can think of, anyway). But I can say this much. The differential dx represents a change from (x,y) to a new point, in the x direction, and dy represents an analogous small change in the y direction. The differential ds represents a change beginning at some point (x,y) and ending at another point,

Computationally, these line integrals are very simple. If curve C can be parametrized according to two functions x(t) and y(t), then just rewrite the integrands like this:

[tex]G(x(t),y(t))\frac{dx}{dt}dt[/tex]

[tex]G(x(t),y(t))\frac{dy}{dt}dt[/tex]

[tex]G(x(t),y(t))\sqrt{(\dfrac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}}[/tex]

And that's how you do line integrals.

Share:

- Last Post

- Replies
- 10

- Views
- 1K

- Last Post

- Replies
- 1

- Views
- 284

- Last Post

- Replies
- 4

- Views
- 432

- Last Post

- Replies
- 29

- Views
- 1K

- Last Post

- Replies
- 5

- Views
- 454

- Last Post

- Replies
- 5

- Views
- 438

- Last Post
- Math POTW for University Students

- Replies
- 11

- Views
- 354

- Last Post

- Replies
- 20

- Views
- 692

- Last Post

- Replies
- 7

- Views
- 363

- Last Post

- Replies
- 4

- Views
- 500