ChapterZero

I started studying last night for my Analysis test this Friday covering Chapters 8 and 9 of baby Rudin— ’some special functions’ and ‘functions of several variables’. Both of them were hard chapters for me, in that I didn’t really get several of the proofs.

Most of the material, I have a feeling, will be from Chapter 9— that seems more important—, and that’s what I had the most trouble with, so I got two books from the library that offered alternate approaches than Rudin’s. I wouldn’t be able to do that for Chapter 8, because how many books have comparable sections on at a level useful to me? On the other hand, lots of books had sections on the Implicit, Inverse, and Contraction mapping theorems (ImInvCont), not to mention functions of several variables.

The two books I picked up: “Mathematical Analysis I” by Vladimir A. Zorich and “Applied Mathematics: Body and Soul [Vol. 3]” by K. Eriksson, D. Estep, and C. Johnson turned out to be excellent choices. The first one is very much rigorous, even to the level of Rudin, but his approach is different enough, and he offers more motivtion than Rudin, that I’m going to finish reading his sections on the ImInvCont when I’m done with Rudin. The only thing I am finding a little off putting about this book is the author’s seeming obsession with notation. Sometimes it seems like he’s trying to recast analysis as a branch of logic.

The second book is in a class of itself. I’m considering reading all the volumes, because I love the approach the authors take of using Lipschitz continuity. I’d never seen it used before, but boy does it make all the proofs much shorter and intuitive. Of course, at the same time, you lose some coverage of pathological cases, but that’s fine by me. Between the intuitive approach in this book and Rudin’s rigour (and rigor mortis :)), I think I’ll be able to pull myself together for the test.