December 2019
Intermediate to advanced
960 pages
25h 46m
English
Content preview from Essentials of Mathematical Methods in Science and Engineering, 2nd Edition
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CHAPTER 17CALCULUS of VARIATIONS
The extremum point of a surface, 
is defined as the point where the first differential, 
vanishes:
Since 
and 
are independent infinitesimal displacements, Eq. (17.1) can only be satisfied when the coefficients of 
and 
vanish simultaneously:
(17.2)
A point that satisfies these conditions is called the stationary point or the extremum point of the surface. To determine whether an extremum corresponds to a maximum or a minimum, one has to check the second differential, 
, which involves second‐order partial derivatives of For a function of independent ...
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