I am the "aim high" type of person, and due to that, if I were to change one thing I did in college, that would be to have NOT taken Calc I and directly have done Calc II.
As of Fall 2012, if an incoming first-year starts doing a BS Physics right away without having any transfer credit, you basically follow this schedule:
- First year
- Fall : Calc I, Intro Phys I
- Spring : Calc II, Intro Phys II, Scientific Computing
- Second year
- Fall : Calc III, Intro Phys III, Elementary Lab I
- Spring : Diff. Eq., Modern Phys, Elem. Lab II
- Third year
- Fall : Classical Mechanics, Quantum Mechanics I, Advanced Calc
- Spring : Electricity and Magnetism I, QM II, Partial Diff. Eq.
- Fourth year
- Fall : Statistical Mechanics, EM II, Intermediate Lab
- Spring : Research, any one 3000-5000 level Elective
What's the big deal about following this schedule?
Following this schedule is perfectly fine. In fact, most undergrads follow this schedule and many got into very decent grad schools.
Here is the point of skipping Calc I. And for this, I'm assuming you want to take challenging upper-level classes asap.
Basically all physics classes are only offered once a year, and some math classes required for the BS are also only offered once per year. These include MATH 3255 Diff. Eq. (Spring), MATH 5210 Adv. Calc. (Fall), and MATH 5220 Partial Diff. Eq (Spring).
Now we consider that you take Calc II in your first-year fall. Calc II is the prerequisite for Diff. Eq., so you will take Diff. Eq. concurrently with Calc III during your first-year spring. Here comes the point. Since you now have the prerequisites for all the third-year physics and math classes, you can go straight to the third-year courses (Class. Mech, QM, etc.) while doing Intro III.
That was kind of obvious. Well... at least from hindsight. So why did I not do that?
The main reason was that I had no transfer credit for that class, even though that was completely high school materials for me.
I come from a foreign country, and my high school math actually covers up to half of Calc II. At that time I was worried that I might need time to acclimate to the new environment, and therefore went the easy way. Bad choice. I did not study for Calc I at all, literally. Finished every homework in an hour, went to mid-terms and finished everything within 20 minutes, and left the finals in an hour because I wanted a bowl of soup. And I still managed to get an easy A+.
I am not trying to be cocky here. Calc I is one of those classes that if you know it, skip it. You will get a lot of practices in physics and other math classes, so you don't have to re-familiarize yourself with basic differentiation and integration by taking Calc I.
Calc I teaches you up to integration by parts, but that will be taught again in Calc II, so if you know everything before that, you are good. Don't bother about the epsilon-delta proof, unless you want to do a second math major. But the proof will be introduced in other proof-based math classes again anyways.
Enough of Calc I, but why do you want to do third-year classes early in your second-year?
Who doesn't want to do exciting physics? Most of the more exciting stuff are in the 5000-levels, and some of them can only be taken if you have done some of the fourth-year stuff in your third year. For example, mathematical methods is at the same time as statistical mechanics for this year (Fall 2012). That was also the same for Fall 2011. If you do stat. mech. in your fourth-year, it would be impossible for you to take mathematical methods. Instead of having your fingers crossed for zero time clashes for your favorite courses, why not start earlier and be ahead in the game?
With Calc I gone, probably your schedule will look like this, considering that you don't take all third-year courses in your second-year:
- First year
- Fall : Calc II, Intro Phys I
- Spring : Calc III, Intro Phys II, Scientific Computing, Diff. Eq.
- Second year
- Fall : Advanced Calc, Intro Phys III, Elementary Lab I, Classical Mechanics
- Spring : Modern Phys, Elem. Lab II, Electricity and Magnetism I, Partial Diff. Eq.
- Third year
- Fall : Quantum Mechanics I, Statistical Mechanics, EM II
- Spring : QM II, Intermediate Lab
- Fourth year
- Fall :
- Spring :
Notice I left some blank spaces up there. You still need to fit research and one 3000-5000 level elective into that. I guess I don't have to tell you where to fit those. There are a lot of good 5000-level courses at UVA, and now you have the freedom to take most, if not all, of those. Plus in this schedule, you can save time from classes in your fourth-year fall for your PGRE and grad school application.
This is a tough course load, but trust me, there are at least a few people doing that every year, and some (like me) regret for not doing that. Exemption from Calc II, relatively, is not a great deal, but Calc I does make a difference.
Conclusion:
Don't let Calc I mess up your four years and reduce your chances of getting into interesting physics classes. Worst comes to worst, when the department says that you need Calc I credits for physics despite that you did partial diff. eq. (total b.s., but unfortunately I heard of someone who had to do that for Calc II), you can always take it in your final semester as a lim(N->infinity)(super)^N easy A+, while doing string theory and general relativity.