I'm currently attending a community college and will probably double major in physics and math. I'm currently taking a multivariable calculus class but I still have a lot of free time since the class is based on a textbook full of exercises and formulas with little proofs. So I was wondering what is the best approach to preparing for future math classes. Since I did not really understand Linear Algebra that well last semester (even though I got an A) and I did not understand Differential Equations well either, I'm thinking that I should go relearn them. The reason I had trouble understanding them so much was because I understood Calculus I very poorly before. But I self-studied Calculus I during the summer and now understand the basic concepts much better than before. I'm still trying to do more self-studying with Calc I, but now I'm trying to learn it more theoretically thorough the text by Apostol. So my question is this: Should I be trying to go through Apostol's Calculus volume I rigorously or going through linear algebra/differential equations first?
What I would do is do through the linear algebra/differential equations. More breadth is better than depth. In analysis, you go deeper anyway.
The best way to learn may is indisputably to do many problems. Crack open the textbooks, and do every problem you can lay your eyes on. If you spot-check your understanding in Apostol, and find that you can solve most of the problems with little effort, go ahead and move onto something more challenging. - Warren