Is calculus not rigorous? While studying single and multivariable calculus during my first year some people complained that calculus wasn't rigorous enough, when I asked about this no one seemed to be able to really specify exactly what was not rigorous about it. So I want to ask if this is true or if my friends tried to be smarty pants? My professors mentioned nothing about this. 
The only such thing I can think of is that we considered $\mathbb{R}$ (and $\mathbb{R}^n$) to be given and just kind of "the number line of every number you possibly can think of". We didn't care about the construction of the reals at all. But I'm pretty sure that this is not what they meant. 
I don't think I will take any sturdy course in real analysis so I want to ask if the standard definitions and proofs involving limits, derivatives, differentiability, continuity, integrals etc one stumbles upon in calculus is somehow "simplified" in calculus and made more formal and "clear" in later and more advanced courses in real analysis?
If this is true, does it exist any good examples which can illustrate this for someone who is slightly afraid of epsilon and deltas? 

Math branches are not more or less rigorous by themselves. What can be more or less rigorous is how you approach them.
You will often see Algebra and Topology as "very rigorous" while Numerical Calculus and Statistics appear "not so rigorous" but there is nothing intrinsically true about that statement. This differences arises from their applications, not the disciplines themselves. In other words, you can make your Statistics (or Calculus, or whatever) as rigorous as you want it to be
