Simplifying a differential equation

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SUMMARY

The discussion focuses on simplifying a differential equation where an extra term, specifically (dA/dx)*(dσ/dx)*dx*dx, arises during multiplication. This term is classified as second order in dx and can be disregarded because dx is an infinitesimal quantity. The primary term retained is first order in dx, which is essential for maintaining the accuracy of the equation.

PREREQUISITES
  • Understanding of differential equations
  • Familiarity with the concept of infinitesimals
  • Basic knowledge of calculus
  • Experience with mathematical notation and terminology
NEXT STEPS
  • Study the properties of infinitesimals in calculus
  • Learn about Taylor series and their applications in simplifying equations
  • Explore the concept of higher-order derivatives
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Mathematicians, physics students, and anyone involved in solving or simplifying differential equations will benefit from this discussion.

mash17
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When I multiply out the first line I end up with an extra (dA/dx)*(dσ/dx). Can someone please show me how i get from the first line to the second. Thanks
 

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The extra term is dA/dx · dσ/dx · dx · dx, which can be dropped because dx is an infinitesimal quantity and this term is second order in dx, infinitesimally smaller than the term you keep, which is first order.
 

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