Multivariable Calculus: Calculus in 4 Dimensions скачать в хорошем качестве

Multivariable Calculus: Calculus in 4 Dimensions

At the end of a multivariable course we are often asked what calculus is like beyond 3 dimensions. This is an attempt to outline multi-variable calculus in four dimensions without assuming any linear algebra pre-knowledge. In particular, we avoid the usual exterior algebra set-up. After motivating 4 dimensional space (it is important in physics, computer vision, division algebras), we look at differential forms and define gradient, curl, hypercurl and divergence in 4D, then tell how to integrate k-forms over k-dimensional objects and finally look at the four integral theorems: FTLI, Stokes, Hyperstokes and divergence theorem in 4 dimensions. A handout to this lecture is here http://people.math.harvard.edu/~knill... Some older handouts: http://people.math.harvard.edu/~knill... or (which uses a tiny bit of linear algebra): http://people.math.harvard.edu/~knill...