Looks to be a multivariate calculus text by the Hubbards:

http://matrixeditions.com/5thUnifiedApproach.html

That's correct (a later edition than the pdf given the date). It is a beautiful book that blends the practical and abstract together to really give a solid foundation in both linear algebra and multivariable calculus topics. If someone asked me for exactly one book to read after learning single variable calculus, this is the book I would recommend. It is long, but extremely satisfying.

It covers in detail many topics often glossed over while keeping an eye on what is actually applicable, including such things as (taken from their page):

> More big matrices! We included the Perron-Frobenius theorem, and its application to Google's PageRank algorithm More singular values! We included a detailed proof of the singular value decomposition, and show how it applies to facial recognition: "how does Facebook apply names to pictures?"

The fifth edition has a similar section in chapter 0: http://matrixeditions.com/UnifiedApproach5thedSamples.html.

Was going to buy a PDF version, but after reading the requirements page [1] I decided not to buy anything from those authors. Also, the 5th edition of this book is not on Amazon.

[1] http://matrixeditions.com/Drumlin.html

Vector Calculus, Linear Algebra, and Differential Forms, A Unified Approach by John H. Hubbard and Barbara Burke Hubbard.

Great Thanks!