• If v (t) = [v1(t), v2(t), v3(t)] = v1(t)**i****j****k ****t****i****j****k**

**(u • v)****u’ • v**** u • v’**

**(u x v)’ = u’ x v + u x v’.**

#### Introduction to Div, Curl, Grad

Divergence, Curl and Gradient

#### Vector Integral Calculus

The analogue of the definite integral of calculus is the line integral

Independence of path of a line integral in a domain D means that the integral of a given function over any path with endpoints A and B has the same value for all paths from A to B that lie in D; here A and B are fixed. An integral (1) is independent of path in D if and only if the differential form with continuous F1, F2, F3 is exact in D. Also, if curl F = 0, where F = [F1, F2, F3], has continuous first partial derivatives in a simply connected domain D, then the integral (1) is independent of path in D.

#### Integral Theorems

These are theorems which will be introduced.

o Green’s theorem in the plane

o Divergence theorem of Gauss

o Green’s formulas

o Green’s formulas

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