How do you choose problem sets in Courant's calculus texts?

[Saqib Ali]

I'm going to use Courant's volume 1 and 2. I don't want to try every problem in the book, so how do I go about choosing problems to know if I understand the material?

 

[Buffu]

I'm going to use Courant's volume 1 and 2. I don't want to try every problem in the book, so how do I go about choosing problems to know if I understand the material?

Some techniques that I use :

A) : Just look at the problems, if they seem hard do it else ditch it.

Eg: 1) $\displaystyle \int_0^\infty \dfrac1{x^2} dx$ and 2) $\displaystyle \int_0^\infty \dfrac{\sin x}{x} dx$. You shouldn't even touch problem 1 but you should definitely try to solve problem 2.

B) : For problems like :
Solve the following differentials equations
1) $y' = x$
2) $y'' + y' = x$
3) $y'' + y' + y = x$.

Here do only problem 3 and leave rest of it.

C) : Don't be stuck on a single problem for more than 30 mins. Leave the problem if you can't do it and come back after few days to it.