Vector Calculus Introduction | By Shreya Mahajan

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Aj k lecture se hm start karenge hamara new chapter " Vector Calculus "

Vector Calculus :
Vector calculus is also known as vector analysis which deals with the differentiation and the integration of the vector field in the three-dimensional Euclidean space.


Some important term discussed in this lecture :

Scalar Function -
Suppose D is any subset of the set of all real numbers. If to each element t of D, we associate by some rule a unique real number f(t), then this rule defines a scalar function of the scalar variable t. Here f(t) is a scalar quantity and thus f is a scalar function.

Vector Function -
Suppose D is any subset of the set of all real numbers. If to each element t of D, are associate by some rule a unique vector f(t), then this rule defines a vector function of the scalar variable t. Here f(t) is a vector quantity and thus fis a vector function.

Scalar Fields - If to each point P(x, y, z) of a region R in space there
corresponds a unique scalar f(P), then f is called a scalar point function and we say that a scalar field has been defined in R. For example, f(x, y, z) = x²y³-3z² defines a scalar field.

Vector Field -
If to each point P(x, y, z) of a region R in space there
corresponds a unique vector f(P), then f is said to be a vector point function and we say that a vector field fhas been defined in R.

In today's lecture we have also discussed the differentiation formulae related to the vecters.

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