I am looking for some suggestions on a good calculus book I shall keep on hand all the time.
I am a graduate student who will be commencing research in the area of theoretical PDE (nonlinear). However I often get stuck on some basic calculus facts where most undergrad knows. My maths background is very applied(financial maths) hence I am lacking the actual preparation to work in theoretical PDE. However, it is too late for me to turn back.
Very often as I feel, research in theoretical discipline (especially the analysis of PDE) requires nothing advanced but rather some delicate calculus and real analysis (perhaps at high school level)
I found Stewart Calculus: concepts and context helpful helpful since we did not learn how to calculate stuff like surface integral (or any those engineering kind). But the book is too big and quite difficult to find a copy from the library (since first year students have the priority)
Spivak is also good. But too little multivariable stuff.
If I can find a book contains all that calculus facts allows one to study functional analytics aspects of nonlinear PDE, would be great!
Any suggestions appreciated.