I underestimated the difficulty of Widder's Advanced Calculus

[flamrim]

I somehow managed to get Bs in two calculus courses and was pretty confident that in a pinch I was capable of doing work involving lagrange multipliers, Green's theorem, convergences of improper integrals, and such. My textbook was multivariable calculus by Larson and Edwards which I was sold forever ago. This semester I just enrolled in a Linear Algebra + Ordinary Differential Equations course so I figured I would need to go back and get a good reference for filling gaps in my knowledge and reviews on Amazon and this forum pointed to Widder as a cheap, highly worthwhile purchase.

I'm having a much harder time with this than I thought I would. Do I need to go back to basics and pretty much relearn calculus? Did those courses I take simply fail to prepare me for serious work? Is there a certain approach I should take with this book? This seems so much more abstract than what I remember doing. I have the Tenenbaum book on ODEs which is just perfect for me and I'm enjoying so far and yet somehow Widder is overwhelming.

I do recall seeing an old post somewhere mentioning a difference between doing Calculus and truly understanding Calculus at a more fundamental level.

 

[qspeechc]

Certainly advanced calculus (i.e. multi-variable calculus) assumes you know single-variable calculus, but Widder's book does not assume you have taken a theoretical and rigorous calculus course.

A nice book to review how to do calculus is Lang's "A First Course in Calculus" which you can get cheaply, and you can even get an older edition. It cuts the crap and presents what you need to know clearly.
If you like that book you can get Lang's other book "Calculus of Several Variables" to complement Widder.

Advanced calculus is obviously more difficult than single-variable calc, so to get the same marks you need to work harder. Browsing through Widder, it seems like a nice book, but do look at Lang, and others if you wish. And you will need to remember the stuff you did in earlier calc courses, so maybe you want to revise that stuff.