Infinitesimal areas and volumes for common structres

In summary, the conversation mainly focused on the difficulties of understanding infinitesimal areas and volumes in the context of gravitational equations. The speaker suggests looking at resources on Khan Academy, specifically under the "Calculus-Based Physics" tab, for tutorials on this topic. They also recommend consulting textbooks on Intermediate Mechanics for derivations of infinitesimal areas and volumes for different shapes. The professor emphasized the importance of this derivation.
  • #1
Shackleford
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We pretty much do derivations maybe 80% of the time in my Intermediate Mechanics class. I'm having a bit of trouble seeing the various infinitesimal areas or volumes when incorporating that into an infinitesimal mass and density equation in our gravitational chapter we're in right now. Is there a website or something that walks through the derivation of infinitesimal area/volume for a spherical shell, sphere, etc.? I was able to fully understand the gravitational force from a spherical shell with areal density and so forth. The professor said this is a very important derivation.
 
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  • #2
I recommend looking at the resources on Khan Academy. They have a great series of tutorials and videos on calculus-based physics topics, including infinitesimal volume and area calculations. You can find these under the "Calculus-Based Physics" tab on the Khan Academy website. Additionally, you may want to look into textbooks that cover Intermediate Mechanics. Many of these textbooks have derivations of various infinitesimal areas and volumes for a variety of shapes.
 

FAQ: Infinitesimal areas and volumes for common structres

What is an infinitesimal area?

An infinitesimal area is a mathematical concept that refers to a very small, but non-zero, area or surface. It is often used in calculus to describe the behavior of functions and to calculate the slope of a curve at a specific point.

How is infinitesimal area calculated?

Infinitesimal areas are typically calculated using the concept of limits in calculus. This involves taking the limit as the size of the area approaches zero, which allows for a more precise calculation of the area.

What are common structures that use infinitesimal areas and volumes?

Infinitesimal areas and volumes are commonly used in various fields of science and engineering, such as physics, engineering, and biology. They are particularly useful for describing the behavior of curves, surfaces, and volumes in these fields.

What are the limitations of using infinitesimal areas and volumes?

One of the main limitations of using infinitesimal areas and volumes is that they are theoretical concepts and cannot be physically measured or observed. Additionally, they may not accurately represent real-world situations, as they rely on the assumption of continuous and smooth functions.

Why are infinitesimal areas and volumes important in science?

Infinitesimal areas and volumes are important because they allow scientists to make precise calculations and predictions about the behavior of various structures and systems. They also provide a way to model and understand complex phenomena in a more simplified manner.

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