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### Vector Differential And Integral Calculus: Theory and Definitions - Differentiation of Vectors, Introduction to Div, Curl, Grad; Vector Integral Calculus; Green’s theorem in the plane; Divergence theorem of Gauss, etc. #### Introduction to VectorsVectors: Introductory Problems and Examples Applying Vectors to Geometric ProblemsVector Applications in 2D and 3D GeometryVector Differential And Integral Calculus: Theory and DefinitionsVector Differential And Integral Calculus: Solved Problem Sets

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Vector Differential And Integral Calculus

#### Differentiation of Vectors

• If v (t) = [v1(t), v2(t), v3(t)] = v1(t)ijk  tijk
(u • v)u’ • v u • v’
(u x v)’ = u’ x v + u x v’.

#### 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

#### Complete Tutorial :

In case you're interested in learning more about Vectors, here's the full set of tutorials we have :

 Vectors 1a ( Theory and Definitions: Introduction to Vectors; Vector, Scalar and Triple Products) Vectors 1b ( Solved Problem Sets: Introduction to Vectors; Vector, Scalar and Triple Products ) Vectors 2a ( Theory and Definitions: Vectors and Geometry ) Vectors and geometry. Parametric vectorial equations of lines and planes. Angles between lines and planes. Co-planar and collinear points. Cartesian equations for lines and planes in 3D. Vectors 2b ( Solved Problem Sets: Vectors and Geometry ) Vectors 3a ( Theory and Definitions: Vector Differential and Integral Calculus ) Vectors 3b ( Solved Problem Sets: Vector Differential and Integral Calculus )