Recommend book to follow Introduction to Analysis by Rosenlicht

[MechanicalEngr]

Recommend book to follow "Introduction to Analysis" by Rosenlicht

I am trying to build a great foundation in analysis before moving into functional analysis, ode and tensor calc( planning on graduate school in computational fluid mechanics ). I love the style of Rosenlichts text. What's the best book to take it to the next level? I seek something very strong in analysis of functions of several real variables and vector analysis... Any suggestions? Does principles of mathematical analysis by rudin cover multivariate and vector functions?

Thanks in advance

 

[MechanicalEngr]

Meant pde, damn iPad!

 

[Bacle2]

I liked "Advanced Calculus of Several Variables" , by C.H Edwards, but I'm doing pure Math. Maybe take a look at it and see if you like it. It has a lot on Differential Forms.