- #1
Derivator
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Hi all,
In thermodynamics one often has equations like
A dx + B dy = ∂f/∂x dx + ∂f/∂y dy
From which follows
A = ∂f/∂x
B = ∂f/∂y
Can anyone explain to me why this conclusion is necessary from a mathematical point of view, please?
Here is my try:
A dx + B dy = ∂f/∂x dx + ∂f/∂y dy
=>
(A-∂f/∂x )dx + (B- ∂f/∂y)dy = 0
since the terms in front of the differentials are independent of each other:
(A-∂f/∂x ) = const_1
(B- ∂f/∂y) = const_2
However, I cannot justify why const_1 = const_2 = 0
Derivator
In thermodynamics one often has equations like
A dx + B dy = ∂f/∂x dx + ∂f/∂y dy
From which follows
A = ∂f/∂x
B = ∂f/∂y
Can anyone explain to me why this conclusion is necessary from a mathematical point of view, please?
Here is my try:
A dx + B dy = ∂f/∂x dx + ∂f/∂y dy
=>
(A-∂f/∂x )dx + (B- ∂f/∂y)dy = 0
since the terms in front of the differentials are independent of each other:
(A-∂f/∂x ) = const_1
(B- ∂f/∂y) = const_2
However, I cannot justify why const_1 = const_2 = 0
Derivator