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

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For Engineering Mathematics - II - Vector Calculus - 2007 any vector field f , and any closed surface S S Curl f . n dS 0 Page 20 of 72
Engineering Mathematics - II - Vector Calculus - 2007 Summary Vector function: A vector function of a scalar variable t is of the form f1(t) i f2 (t) j f3(t) k Differentiation of a Vector: d f df 1 df df i 2 j 3 k dt dt dt dt Equation of a space curve: Equation of a space curve is represented by r (t) x(t) i y(t) j z (t) k d r Velocity : dt space curve. is the velocity v and is along the tan gent to the Unit tan gent vector : t d r dt d r | | dt Unit normal : n | d t ds d t | ds is called the unit normal to the curve. Scalar field: A scalar corresponding to each (x,y,z) in a region R. Vector field: A vector corresponding to each (x,y,z) in a region R r f1 (x, y, z) i f2 (x, y, z) j f3(x, y, z) k Gradient: If is a scalar field then i x j y k z is called the gradient of . Unit Normal to the surface : If = c is a surface then | | n is the unit normal to the surface. Page 21 of 72
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Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...

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