in which field vector calculus is applied deeply
For Literally Everything.
High SchoolCalculus AB - Calculus 1Calculus BC - Calculus 1 + part of Calculus 2College:Calculus 1: Single variable calculusCalculus 2: Multi-variable CalculusCalculus 3: Vector CalculusCalculus 4: Differential Equation
Engineering careers, physicists, mathematicians, economists.
Once you've completed differential and integral calculus, multivariable calculus is often next step, and beyond that there is advanced calculus which generalizes calc to multidimensional spaces and uses vector-valued functions. Often concurrent with high level calculus in college courses is linear algebra and differential equations. There's nothing really 'after' calculus, because any topic in mathematics has a myriad of problems, theories, and potential applications to be explored. Calculus is, however, normally the highest level of math taught in US high schools and is a basic required course for any science/engineering major in college.
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.
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.
CALCULUS
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.
Measures of motion (displacement, velocity, acceleration) and forces are all vectors so any study involving these would require vector calculus.
It is a tool for an engineer. I am a mechanical engineer, and you MUST know your calculus to be able to get through it, or through physics with calc. Good luck!
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.
Being a contractor or a builder. It makes a lot of money and involves math, and you also get some exercise. This job involves math. Other jobs are: Pharmacy ( elementary calculus) Architecture (nothing beyond trig is required ) Accounting ( business calculus, applied linear algebra and beginning computer programming) Physics ( vector calculus and differential equations) Medicine ( not so much, enough calculus for physics and statistics) Engineering (calculus, differential equations, vector calculus) Physical chemistry Aviation (spherical trig )
Richard H. Crowell has written: 'Calculus of vector functions' -- subject(s): Vector analysis 'Calculus with analytic geometry' -- subject(s): Analytic Geometry, Calculus
H. K. Nickerson has written: 'Advanced calculus, by H.K. Nickerson, D.C. Spencer and N.E. Steenrod' -- subject(s): Calculus, Vector analysis 'Advanced calculus' -- subject(s): Calculus, Vector analysis