- #1

Pythagorean

Gold Member

- 4,210

- 270

This isn't directly a request for homework help, since classes won't be starting for another two months, but I suppose it will be helpful to homework because I'll be taking Applied Analysis, Mechanics, and Electromagnetism, all of which include vector calculus.

Given time, I will try to work through a Vector Calculus book here.

I'm currently reading "Div, Grad, Curl, and All That" and already having trouble intepreting some of the equations in chapter 1, even though I've taken all the required courses for it. It may have slipped my mind, but here goes the questions.

(i use vector signs for hats)

[tex]

F(x,y) = \vec{i} x + \vec{j} y

[/tex]

I'm not able to coneptualize how the above equation appears as vectors always flowing away from origin (the corresponding graph shown in the book). I'm guessing that vector function is not simply a vector like I'm assuming it is, but either way, there should be two points right? One for the base of the vector and one for the head. But I can only conceptualize this if the origin is always the base (which doesn't seem the case in the illustration)

The other one:

[tex]

G(x,y) = \frac {\vec{-i} y + \vec{j} x}{\sqrt{x^2+y^2}}

[/tex]

which is supposed to represent a set of vectors flowing radially, counterclockwise. I can see the presence of a circle in the equation, but I'm still a bit sketchy as to how you would work out the shape/size of the arrow based on numbres substituted in for x and y.

Given time, I will try to work through a Vector Calculus book here.

I'm currently reading "Div, Grad, Curl, and All That" and already having trouble intepreting some of the equations in chapter 1, even though I've taken all the required courses for it. It may have slipped my mind, but here goes the questions.

(i use vector signs for hats)

[tex]

F(x,y) = \vec{i} x + \vec{j} y

[/tex]

I'm not able to coneptualize how the above equation appears as vectors always flowing away from origin (the corresponding graph shown in the book). I'm guessing that vector function is not simply a vector like I'm assuming it is, but either way, there should be two points right? One for the base of the vector and one for the head. But I can only conceptualize this if the origin is always the base (which doesn't seem the case in the illustration)

The other one:

[tex]

G(x,y) = \frac {\vec{-i} y + \vec{j} x}{\sqrt{x^2+y^2}}

[/tex]

which is supposed to represent a set of vectors flowing radially, counterclockwise. I can see the presence of a circle in the equation, but I'm still a bit sketchy as to how you would work out the shape/size of the arrow based on numbres substituted in for x and y.

Last edited: