Modern conceptual treatment of multivariable calculus, emphasizing the interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. At the same time, ample attention is paid to the classical applications and computational methods. Hundreds of examples, problems and figures. 1973 edition.
This book was difficult, and required for an Advanced Calculus uni course. Exercises can be really difficult to really easy. It felt dated, had unnecessary assumptions for some things. The defining of the Riemman integral was wonky. This was my first exposure to differential forms, and it was hard to make sense of, my professor sort of lectured from the book but also not really. I had a separate book Bachman's differential forms book, it was far clearer than this, but they muddle the other. It's an okay book. I don't know that I would recommend it to anyone, especially if it's your only source.
Being a huge math person and analyst, this is one of my favorite books! You do need to remember your Calculus methods to understand what is going on. It is definitely a book that needs a "helping hand" to review the equations and methods of Calculus.