Vector calculus is applied in electrical engineering especially with the use of electromagnetics. It is also applied in fluid dynamics, as well as statics.
Mechanical engineering usually deals with forces and their effects on materials. Forces are vectors and so, to study their effects you need to use vector calculus.
Vector Algebra and Vector Calculus are used widely in science, especially Physics and engineering.The physical world involves four dimensions, one scalar dimension and three vector dimensions. From this you can say that 3/4 of the world involve vectors.
Hence the reason for why it is called Vector Calculus, Vector Calc. is simply an expansion in the calculus subject are in math. It deals with Taylor's Formula (in calc 2 you learn the taylor polynomial and the taylor series), theorems from Green, Gauss, and Stokes, and much more.
Measures of motion (displacement, velocity, acceleration) and forces are all vectors so any study involving these would require vector calculus.
One uses calculus including differential equations and vector calculus in the undergrad courses which is as far as got.
in which field vector calculus is applied deeply
Electromagnetic fields, gravitational fields and fluid flow. If you are an engineer you will come across vector calculus to handle three dimensional space.
The theory of radio waves and waveguides is explained in terms of equations in the form of vector calculus. Examples are Maxwell's equations.
Mechanical engineering usually deals with forces and their effects on materials. Forces are vectors and so, to study their effects you need to use vector calculus.
It is used to position an object in3D
The area vector in vector calculus represents the direction and magnitude of a surface area. It is important in applications such as calculating flux, which measures the flow of a vector field through a surface. The area vector helps determine the orientation of the surface and is crucial for understanding the behavior of vector fields in three-dimensional space.
in electrical engineering
The significance of the divergence of a scalar times a vector in vector calculus is that it simplifies to the scalar multiplied by the divergence of the vector. This property is important in understanding how scalar fields interact with vector fields and helps in analyzing the flow and behavior of physical quantities in various fields of science and engineering.
That depends on what your "real life" consists of. If you sell merchandise at a supermarket, or do carpentry work, you won't need such advanced mathematics. If you work in the engineering fields, you might need it at some moment like with electromagnetic fields, gravitational fields and fluid flow. If you are an engineer you will come across vector calculus to handle three dimensional space.
Vector Algebra and Vector Calculus are used widely in science, especially Physics and engineering.The physical world involves four dimensions, one scalar dimension and three vector dimensions. From this you can say that 3/4 of the world involve vectors.
The applications are in transport phenomena, in determining the direction of flow in momentum transport, heat transfer, and mass flux.
Hence the reason for why it is called Vector Calculus, Vector Calc. is simply an expansion in the calculus subject are in math. It deals with Taylor's Formula (in calc 2 you learn the taylor polynomial and the taylor series), theorems from Green, Gauss, and Stokes, and much more.