Question re: difference between Δx and dx

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SUMMARY

The discussion clarifies the distinction between Δx and dx in the context of calculus and physics. Δx represents a finite change between two points, specifically defined as x2 - x1, while dx denotes an infinitesimal change in x, crucial for determining slopes on curves. The equations dL = L0αdT and ΔL = L0αΔT illustrate the difference between differential and finite changes in length due to temperature variations. Understanding these concepts is essential for applying calculus in physics, particularly in slope calculations using methods like the tangential and secant rules.

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  • Understanding of basic calculus concepts, including derivatives and limits.
  • Familiarity with physics principles related to thermal expansion.
  • Knowledge of slope calculations and their significance in graphing functions.
  • Experience with interpreting mathematical notation and equations.
NEXT STEPS
  • Study the concept of limits in calculus to deepen understanding of infinitesimals.
  • Learn about the application of derivatives in physics, particularly in motion analysis.
  • Explore the tangential and secant rules in more detail for slope determination.
  • Investigate the implications of thermal expansion in engineering and material science.
USEFUL FOR

This discussion is beneficial for students studying calculus and physics, educators teaching these subjects, and professionals in engineering fields who require a solid grasp of differential calculus and its applications in real-world scenarios.

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Homework Equations



dL = L0αdT

ΔL = L0αΔT

These two equations are both listed separately on my equation sheet. How are the dL and ΔL terms different?
 
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I think that Δx could just indicate a change in something. In physics for example,
Δx = x2 - x1

dx however, indicates the infinitesimal change in x.
 
Take for instance a curved line.
You want to find the slope m of the curve at point (x,y).

There are a few procedures such as the tangential rule or the secant rule.

But simplictically, assume x is midway between 2 points x1 and x2, and y is midway between corrsponding points y1 and y2.
Then m = (y2-y1)/(x2-x1)
Or, m= Δy / Δx ( if y2-y1 and x2-x1 are not too great )

As Δx or Δy is made to become smaller and smaller to the limit of approaching 0(zero)
Then m=dx/dy
 

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