Ogilvie 



MISCELLANEOUS CONVENTIONS 



1) Velocity Potential : The velocity is always the positive gradient 



of the potential function, 



2) Coordinates and Orientation; In problems involving a steady 



incident flow, that flow is always in the positive x direction. 

 The vertical axis is the y axis in 2- D problems , the z 

 axis in 3-D problems, 



3) Time Dependence: In problems of sinusoidal oscillation, the 



time dependence is always in the form of the exponential 

 function, e'<^*. In such problem.s , the real part only is 

 intended to be used, but we do not indicate this explicitly in 

 general. 



4) Fourier Transforms: These are denoted by an asterisk. For 



example , 



o-*(k) = \ dx e-*'*V(x) ; o-(x) = 4" \ ^k e"^" a*(k); 

 J.oo ^^J-oo 



♦* p®/><» -i(kx*iy) 



^ (k,i;z) = \ \ dx dy e (^(x.y.z). 



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5) Principal-Value Integrals ; These are denoted by a bar through 



the integral sign: 



J. 



"° de f(e) 



6) Order Notation; There are three symbols used: O. o,~. 



a) "y = 0(x)" means: |y/x| < M as x -♦ , where M is 

 a constant not depending on x. 



b) "y = o{x)" m.eans: |y/x| -^0 as x -♦ 0. 



c) " y ~ f(x) " means |y - f{x) | = o(f(x)) as x — 0. 



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