SK ACADEMY|ENGINEERING TUITION,GATE …
Unit 2- Vector Calculus
Formula List
1. The vector differential operator , ([pic]
2. Gradient of a scalar point function , ([pic]
3. Directional Derivative of [pic] in the direction of [pic] is [pic]
4. Maximum Directional Derivative of [pic] is | [pic] |
5. Unit normal vector [pic][pic]= [pic]
6. Angle between two surfaces is [pic]
7. Two surfaces are cut orthogonal then[pic].[pic]=0
8. Divergence of [pic]=[pic][pic] = [pic] where [pic]
9. Curl of [pic]= [pic]x [pic] =[pic] where [pic]
10. If [pic][pic]=0 then [pic] is said to be Solenoidal Vector
11. If [pic]x [pic]=[pic] then [pic] is said to be Irrotational Vector
12. If [pic]x [pic]=[pic] then there exists a scalar point function (Scalar Potential) s.t [pic]= [pic]
13. Laplacian operator [pic]
14. Green’s Theorem
If P, Q, [pic]are continuous and single valued functions of x, y in a closed region R enclosed by a curve C, then [pic]
15. Stoke’s Theorem
The surface integral of the normal component of the curl of a vector function [pic] over an open surface S is equal to the line integral of the tangential component of [pic] around the closed curve C bounding S. (i.e.) [pic]
16. Gauss Divergence Theorem
The surface integral of the normal component of a vector function [pic] over a closed surface S enclosing a volume V is equal to the volume integral of the divergence of [pic] taken throughout the volume V. (i.e.) [pic], where [pic] is the unit outward normal to the surface S.
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