The applications are in transport phenomena, in determining the direction of flow in momentum transport, heat transfer, and mass flux.
The theory of radio waves and waveguides is explained in terms of equations in the form of vector calculus. Examples are Maxwell's equations.
name as many scalar fields and vector fields as u can?
Both, E=Es + Ev = cB therefore, B= Es/c + Ev/c = Bs + Bv. The electric and magnetic fields are quaternion fields consisting of a scalar field and a vector field. Contemporary Physics has not realized this yet. Correct Relativity Theory is a manifestation of quaternion fields, consisting of a scalar field and three vector fields. This shows up in the Energy Momentum four vector, E= Es +cmV. Actually the Lorentz Force is both scalar and vector: F=qvB = - qv.B + qvxB it makes no sense consider only qvxB and to ignore qv.B.
"Vector" is an agent that can carry a DNA fragment into a host cell. If it is used for reproducing the DNA fragment, it is called a "cloning vector". If it is used for expressing certain gene in the DNA fragment, it is called an "expression vector".
import java.util.Vector; public class VectorTest { /** * @param args */ public static void main(String[] args) { //instantiating a vector Vector vct = new Vector(); //Add objects to a vector vct.add("One"); //getting values from the vector String val = (String) vct.get(0); //vector size System.out.println("Vector size is: " + vct.size()); //removing elements from a vector vct.remove(0); } }
Electromagnetic fields, gravitational fields and fluid flow. If you are an engineer you will come across vector calculus to handle three dimensional space.
in which field vector calculus is applied deeply
Vector calculus is applied in electrical engineering especially with the use of electromagnetics. It is also applied in fluid dynamics, as well as statics.
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.
The answer depends on the context. The applications will vary from one context to another. There are agricultural fields. There are vector fields in physics which depict the magnitudes and directions of forces. There are algebraic structures called fields which have some mathematical properties associated with them.
The theory of radio waves and waveguides is explained in terms of equations in the form of vector calculus. Examples are Maxwell's equations.
name as many scalar fields and vector fields as u can?
U. Koschorke has written: 'Differential Topology' -- subject(s): Congresses, Differential topology 'Vector fields and other vector bundle morphisms' -- subject(s): Singularities (Mathematics), Vector bundles, Vector fields
Both, E=Es + Ev = cB therefore, B= Es/c + Ev/c = Bs + Bv. The electric and magnetic fields are quaternion fields consisting of a scalar field and a vector field. Contemporary Physics has not realized this yet. Correct Relativity Theory is a manifestation of quaternion fields, consisting of a scalar field and three vector fields. This shows up in the Energy Momentum four vector, E= Es +cmV. Actually the Lorentz Force is both scalar and vector: F=qvB = - qv.B + qvxB it makes no sense consider only qvxB and to ignore qv.B.
in electrical engineering
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.
Robert H. Roussarie has written: 'Bifurcations of planar vector fields and Hilbert's sixteenth problem' -- subject(s): Bifurcation theory, Vector fields