I am going to start studying the analysis texts (Rudin-PMA, Apostol-MA, Pugh-RMA) on the first week of August. I have a good proof skills through working on Artin's Algebra and Hoffman/Kunze's Linear Algebra, but I unfortunately only took computational 1-variable calculus (Lang's A First Course in Calculus), and I did not take multivariable calculus, which I might take concurrently with Analysis I and Theoretical Linear Algebra on the upcoming Fall.
I am looking for a brief text which explains the key ideas from both 1-variable and multivariable calculus, one I can read and jump directly into the analysis texts. Could you recommend one?
Also will my lack of multivariable calculus be a problem when I tackle those analysis texts? I seem to understand at least the beginning chapters.