By David Bachman
The smooth topic of differential varieties subsumes classical vector calculus. this article offers differential types from a geometrical point of view available on the complex undergraduate point. the writer methods the topic with the concept complicated recommendations will be equipped up by way of analogy from less complicated situations, which, being inherently geometric, frequently should be most sensible understood visually.
Each new idea is gifted with a common photograph that scholars can simply grab; algebraic homes then stick with. This allows the advance of differential varieties with out assuming a historical past in linear algebra. through the textual content, emphasis is put on purposes in three dimensions, yet all definitions are given in order to be simply generalized to better dimensions.
The moment variation features a thoroughly new bankruptcy on differential geometry, in addition to different new sections, new workouts and new examples. extra ideas to chose routines have additionally been integrated. The paintings is acceptable to be used because the basic textbook for a sophomore-level classification in vector calculus, in addition to for extra upper-level classes in differential topology and differential geometry.