- #1

ericm1234

- 73

- 2

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.

In summary, on pages 14-15, the authors derive the normal vector to a surface by cutting the surface with a plane and then using the curve 'c' in the xz plane. They then want to use the components of 'u' but they have a problem because 'u sub x' in the x direction is not a vector but a function that is equal to 'partial f/partial x times U sub X'.

- #1

ericm1234

- 73

- 2

Physics news on Phys.org

- New quantum error correction method uses 'many-hypercube codes' while exhibiting beautiful geometry
- Researchers advance new class of quantum critical metal that could advance electronic devices
- Researchers make sound waves travel in one direction only, with implications for electromagnetic wave technology

- #2

HallsofIvy

Science Advisor

Homework Helper

- 42,988

- 975

"on pages 14-15" ofericm1234 said:

If u

- #3

ericm1234

- 73

- 2

Let me rephrase:

there is a surface S in 3-d (x, y, z). This is cut by a plan parallel to the xz plane. This intersection of the plane and surface creates a curve C.

Now there is a picture showing the x and z axes with this curve C, and a tangent vector called U. U is decomposed into U sub X and U sub Z HOWEVER, U sub Z is 'equal' here to as 'partial f/ partial x' times U sub X.

So my question is why is U sub Z equal to partial f/partial x time U sub X.

- #4

ericm1234

- 73

- 2

The main concept of "Div Grad Curl and All That" is to introduce the fundamental ideas of vector calculus, specifically the concepts of divergence, gradient, and curl, and how they relate to physical phenomena.

Div, grad, and curl have many applications in fields such as physics, engineering, and mathematics. They are used to describe the behavior of fluids, electric and magnetic fields, and the motion of particles, among other things.

One example is the use of curl to describe the rotation of a fluid in a vortex. Another example is the use of gradient to determine the path of steepest descent in a topographical map.

The relationship between div, grad, and curl is described by the fundamental theorem of calculus for vector fields. It states that the curl of a gradient is always zero, and the divergence of a curl is always zero.

To improve your understanding of div, grad, and curl, it is important to practice solving problems and applying these concepts in different scenarios. Reading additional materials and seeking help from a tutor or teacher can also be helpful.

- Replies
- 4

- Views
- 2K

- Replies
- 1

- Views
- 864

- Replies
- 1

- Views
- 2K

- Replies
- 3

- Views
- 2K

- Replies
- 2

- Views
- 1K

- Replies
- 3

- Views
- 1K

- Replies
- 3

- Views
- 1K

- Replies
- 2

- Views
- 2K

- Replies
- 2

- Views
- 2K

- Replies
- 10

- Views
- 2K

Share: