O'Reilly logo

A Course in Mathematical Analysis by D. J. H. Garling

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

17

Differentiating functions of a vector variable

17.1 Differentiating functions of a vector variable

In Part Two, we considered continuity and limiting properties of real-valued functions of a real variable – functions defined on a subset of R. In Part Three we extended these ideas to functions between metric spaces, or between topological spaces. In particular, these results apply to functions of several real variables – functions defined on a subset of Rd.

We now turn to differentiation. This involves linearity: we therefore consider functions defined on a subset U of a real normed space (E, ||.||E) taking values in a real normed space (F, ||.||F). In fact, our principal concern will be with functions of several real variables (functions defined ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required