Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...

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C Engineering Mathematics - II - Vector Calculus - 2007 f .d r represents the work done in moving a particle of unit along the Curve C from A to B. mass Surface Integral of a vector function The surface int egral of f over a surface S is defined as S f .n dS where n is the unit normal to the surface S and dS = dx dy Physical Meaning: The surface int egral of f gives the total normal flux through a surface. Volume integral of a vector function The volume int egral of f over a volume V is defined as V f dV f1d V i f2 dV j d V k V V V Integral Theorems Green's Theorem (Statement only) Let M(x,y) and N(x,y) be two functions defined in a region A in the xy plane with a simple closed curve C as its boundary then C (M dx Mdy) N x A M dx dy y Strokes Theorem (Statement only) Let S be an open surface bounded by a simple closed curve C for a field Page 18 of 72
f defined Engineering Mathematics - II - Vector Calculus - 2007 over a region containing S and C. C f .d r S (Curl f ) .n dS Gauss Divergence theorem (Statement only) Let S be the closed boundary surface of a region of Volume V. Then for a vector field f defined in V and on S. S f .n dS S i.e., in Cartesian form div f dV f f f 1 dx dy dz x y z V f dy dz f 1 2 3 2 dz dx f3 dx dy S Note: Page 19 of 72
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Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...

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