Vector Calculus Formulas
For a vector field given as F(x,y,z) = p(x,y,z)i + q(x,y,z)j + r(x,y,z)k. The following formulas are given.
Fundamental Theorem of Line Integral
if F = ∇Φ and Curve C has A and B endpoints then its line integral is given as
∫cF.dr = Φ(B) – Φ(A)
Circulation Curl Form
There are two theorems under Circulation Curl Form, namely the Green theorem and Stokes theorem.
Green Theorem: If D is the region bounded by curve C then, ∮cF.dr = ∬D(∂Q/∂x – ∂P/∂y)dA
Stoke’s Theorem: For a surface S bounded by curve C stokes theorem given by ∮cF.dr = ∬S(∇ ⨯ F)dS
Flux Divergence Theorem
The Flux Divergence Form of Green’s Theorem is given as ∬D∇. F dA = ∮cF.n ds
The Flux Divergence Form of Stoke’s Theorem is given as ∭D ∇. F dV = ∯sF.n dσ
Vector Calculus in Maths
Vector Calculus in maths is a sub-division of Calculus that deals with the differentiation and integration of Vector Functions. We already know that Calculus is a branch of mathematics that deals with the rate of change of a function concerning another function. There are two major divisions of Calculus namely, Differential Calculus and Integral Calculus.
The branch of Differential Calculus deals with the process of finding derivatives or differentiation of functions while Integral Calculus deals with finding the antiderivative of a function whose derivative is given. In this article, we will learn in detail about Vector Calculus which is a lesser-known branch of calculus, and the basic formulas of Vector Calculus.
In this article, you are going to read everything about what is vector calculus in engineering mathematics, vector calculus formulas, vector analysis, etc.
Table of Content
- What is Vector Calculus?
- Operation in Vector
- Divergence and Curl
- Vector Calculus Formulas
- Vector Calculus Identities
- Vector Calculus Applications
- Solved Examples
- FAQs
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