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Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields, and fluid flow.
Vector calculus is also known as vector analysis. The vector fields are the vector functions whose domain and range are not dimensionally related to each other. The branch of Vector Calculus corresponds to the multivariable calculus which deals with partial differentiation and multiple integration.
16.0: Prelude to Vector Calculus. In this chapter, we learn to model new kinds of integrals over fields such as magnetic fields, gravitational fields, or velocity fields. We also learn how to calculate the work done on a charged ….
In vector (or multivariable) calculus, we will deal with functions of two or three variables (usually x,y or x,y,z, respectively). The graph of a function of two variables, say, z=f(x,y), lies in Euclidean space, which in the Cartesian coordinate system consists of all ordered triples of real numbers (a,b,c).
• Jerrold Marsden and Anthony Tromba, “Vector Calculus” Schey develops vector calculus hand in hand with electromagnetism, using Maxwell’s equations as a vehicle to build intuition for differential operators and integrals.
David Tong: Lectures on Vector Calculus. These lectures are aimed at first year undergraduates. They describe the basics of div, grad and curl and various integral theorems. The lecture notes are around 120 pages.
This plane vector field involves two functions of two variables. They are the compo- nents M and N, which vary from point to point. A vector has fixed components, a vector field has varying components. A three-dimensional vector field has components M(x, y, z) and N(x, y, z) and P(x, y, 2).