ENG 103 - Total differentials

ENG 103 - Total differentials - UNIVERSITY OF CALIFORNIA...

This preview shows pages 1–2. Sign up to view the full content.

U NIVERSITY OF C ALIFORNIA D AVIS College of Engineering ENG 103: Fluid Mechanics J.-P. Delplanque Total (Exact) Differentials Definition If ) , ( y x F is a function of two variables, then the total differential of F is: dy y F dx x F dF ! ! + ! ! = Inverse problem Consider two functions ) , ( y x P and ) , ( y x Q which satisfy the following equation: dy y x Q dx y x P D ) , ( ) , ( + = Under which conditions is there a function ) , ( y x F for which D is the total differential (i.e., dF D = )? dF D = can be re-written: dy y F dx x F dy y x Q dx y x P ! ! + ! ! = + ) , ( ) , ( which leads to ) , ( y x P x F = ! ! and ) , ( y x Q y F = ! ! Since we know that for functions with continuous second order derivatives x y F y x F ! ! ! = ! ! ! 2 2 , a necessary condition for such a function ) , ( y x F to exist is: x Q y P ! ! = ! ! (it turns out that this condition is both necessary and sufficient).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
U NIVERSITY OF C ALIFORNIA D AVIS College of Engineering ENG 103: Fluid Mechanics J.-P. Delplanque
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 2

ENG 103 - Total differentials - UNIVERSITY OF CALIFORNIA...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online