And who doesn’t want that? In vector (or multivariable) calculus, we will deal with functions of two or three variables (usually x,y or x,y,z, respectively). Math should be a tool for clearly stating what we already know. 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). Vector Calculus, also known as vector analysis, deals with the differentiation and integration of vector field, especially in the three-dimensional Euclidean space. They spring up naturally from our definition of circulation as "pushing force along a path" and curl as "pushing force/area". The American physicist J. Gibbs gave vector calculus its modern form. Think of flux as the amount of something crossing a surface. Vector fields represent the distribution of a vector to each point in the subset of space. Your vector calculus math life will be so much better once you understand flux. The fundamentals of vector calculus were laid by the British mathematician W. Hamilton and the German mathematician G. Grassmann in their work on hypercomplex numbers (1844-50). Their ideas were used by the British physicist J. C. Maxwell in his work on electricity and magnetism. This “something” can be water, wind, electric field, bananas, pretty much anything you can imagine. Vector Calculus: Understanding Circulation and Curl. Vector calculus is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus. Physical Intuition. Vector calculus (or vector analysis) is a branch of mathematics concerned with differentiation and integration of vector fields, primarily in 3 dimensional Euclidean space The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which includes vector calculus as well as partial differentiation and multiple integration. Vector Calculus Definition.

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