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VECTOR CALCULUS - Coggle Diagram
VECTOR CALCULUS
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LINE,SURFACE AND VOLUME INTEGRALS
Del OPERATOR
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IS NOT A VECTOR IN ITSELF,BUT WHEN IT OPERATES ON A SCALAR FUNCTION,THE PRODUCT IS A VECTOR
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GRADIENT OF A SCALAR
THE GRADIENT OF A SCALAR field V is A VECTOR THAT REPRESENTS BOTH THE MAGNITUDE AND THE DIRECTION OF THE MAXIMUM SPACE RATE OF INCREASE of V
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DIVERGENCE THEOREM
THE TOTAL OUTWARD FLUX OF A VECTOR field A through a CLOSED surface S is THE SAME AS THE VOLUME INTEGRAL OF THE DIVERGENCE of A.
NOTE : A CLOSE SURFACE INSIDE A VECTOR FIELD HOLDS NO NET FLUX; THE TOTAL FLUX INTO THE SURFACE WILL GO OUT OF THE SURFACE COMPLETELY!
CURL OF VECTOR
THE CURL of A IS AN AXIAL (OR ROTATIONAL) VECTOR WHOSE MAGNITUDE IS THE MAXIMUM CIRUCLATION of A per unit AREA AS THE AREA LENDS TO ZERO AND WHOSE DIRECTION IS THE NORMAL DIRECTION OF THE AREA WHEN THE AREA IS ORIENTED SO AS TO MAKE THE CIRCULATION MAXIMUM
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STROKE'S THEOREM
STATES THAT THE CIRCULATION OF A VECTOR field A around a (closed) path L is equal to the SURFACE INTEGRAL OF THE CURL of A over the open surface S bounded by L provided that A and .... are continuous on S.
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