2 votes

Why stopping at the first derivative in conservation equations?

Great question, ultimately related to the definitions of derivatives and integrals using limits and the fundamental theorem of calculus. Not a mathematician, so things might be informal and a bit ...
R. H.'s user avatar
  • 91
1 vote
Accepted

Partial derivative of change in state with respect to multiplicative faults

I agree with you, and I think this is simply an inconsequential mistake from the book, since in the proof, this result is only an intermediate step, and it is later evaluated at $\theta_{A_i} = 0$.
gdcvdqpl's user avatar
  • 128
1 vote

Obtaining equation from real life

TL;DR: Real life equations are created by carefully observing relationships between different quantities, making simplification assumptions, and then abstracting them into a mathematical form. I've ...
NMech's user avatar
  • 24.3k

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