Any book the elucidates the use of diffirentials?

[ronaldor9]

The trouble I have in reading mechanic books, at least the ones I have, is that they manipulate diffirentials as though they are algebraic symbols. Now, I know that typically the first year calculus student is told that the differential operator is to be viewed as one symbol and not the quotient of two diffirentials. Are there any books that can elucidate, and justify, the manipulation of diffirentials in such a manner without being too bogged down in rigor; or would I have to wait to study differential manifolds which I presume does place rigor in such manipulations?

 

[Daverz]

Here you go:

http://www.math.wisc.edu/~keisler/calc.html

 

[charng]

There are definitely books that can provide a deeper understanding of the use of differentials without being too bogged down in rigor. One recommendation would be "Calculus: Early Transcendentals" by James Stewart. This book offers a thorough treatment of differentials and their manipulation, while also providing clear explanations and examples. Another option is "Calculus" by Michael Spivak, which delves into the theoretical aspects of differentials but also includes practical applications and examples. Both of these books would be suitable for a first-year calculus student looking to gain a better understanding of the use of differentials.

If you are interested in a more rigorous treatment of differentials, then studying differential manifolds would be a good option. This branch of mathematics deals with more advanced concepts and techniques related to differentials, and would provide a deeper understanding of their manipulation. However, it is not necessary to wait until you study differential manifolds in order to gain a better understanding of differentials. The books mentioned above, as well as other calculus textbooks, can provide a solid foundation that will prepare you for more advanced studies.