Can I Pass Calculus III Without Taking Calculus II First?

[captain math]

Hey guys,

I'm facing a tough decision and I would like to ask you for some guidance and tips regarding my situation.

I want to apply for econ grad school this fall and I'm missing some math essentials. The program I followed did not put so much emphasis on the mathematical background, which is a pity. I figured I need at least Calculus III for any program I would like to apply for. During my undergrad I did Calc I. Nothing else. I would like to use the summer to do Calc III in a 5 week course, since I don't have enough time to get Calc II done, before.

The curriculum of the Calculus course I want to take looks as follows:

Vectors and the Geometry of Space
Cylinders and Quadric Surfaces
Vector Functions
Partial Derivatives
Multiple Integrals
Vector Calculus
Differential Equations

My question is: Do I have a realistic chance to pass Calc III, without having done Calc II? Also, does it build heavily on Calc II or is there a lot of new material?

Thanks for your help!

Captain Math

 

[fluffy123]

I think it's doable. But you'll have to go over polar coordinates and integration techniques.

 

[zcd]

A lot of calc 2 is on integration techniques which don't appear in calc 3 that often. What calc 2 typically covers that is a little more directly relevant to calc 3 is the use of polar coordinates and parametric equations. If you intend to start from calc 3, it would be a good idea to give a look at changing between coordinate systems.

That being said, even though integration techniques aren't directly used in calc 3, they do give a sort of mental training for solving problems in several steps that calc 1 doesn't have.

 

[fluidistic]

Err guys correct me if I'm wrong but calculus 2 should teach you what an integral is! So it's much more than just integral techniques!
Thus assuming you haven't dealt with integrals yet, you should learn (well) what an integral is, dig through the fundamental theorem of calculus and at least learn integration by parts -there's a multivariable version of it-.
When learning about partial derivatives I guess you'll be assigned problems with limits of functions of several variables. I personally found out these limits harder to determine than with function of several variables. Knowing well the epsilon-delta arguments was a must for the course called "calculus 3" at my university. So you might want to refresh your memory of calculus 1 on this too.
It'd be nice if you could see your assignment that you'll get. Or the one that was given last year to calculus 3 students in your university.

 

[eumyang]

Err guys correct me if I'm wrong but calculus 2 should teach you what an integral is! So it's much more than just integral techniques!

Not so. In many Calculus sequences you begin to learn the integral at the end of Calculus I.

 

[Sankaku]

A lot of calc 2 is on integration techniques which don't appear in calc 3 that often.

Then again, a lot of Calc 2 is on subjects that are used all the time in Calc 3. Unless you are a prodigy, one way or another you will need to spend the effort to cover the material in Calc 2. Yes, Calc 3 is more fun, but you will forever be at a disadvantage if you have not mastered the material in Calc 2. There is a reason it is taught in order.

 

[zcd]

Err guys correct me if I'm wrong but calculus 2 should teach you what an integral is! So it's much more than just integral techniques!
Thus assuming you haven't dealt with integrals yet, you should learn (well) what an integral is, dig through the fundamental theorem of calculus and at least learn integration by parts -there's a multivariable version of it-.

I took the calc 1 and 2 AP equivalents in high school and the integrals were introduced towards the middle of calc 1. By calc 2 we were assumed to have a good grasp on substitution.

It might help to also get a catalog description on the calc 2 from OP cause it may vary from school to school.

 

[cjl]

Calc 3 involves a decent amount of integration, and although it isn't quite as dependent on specific integration techniques as calc 2 is, it still assumes a pretty comfortable working knowledge of integrals and methods of solving them. As a result, you'd definitely need to spend some time getting up to speed with calc 2 before tackling calc 3. Is it possible to do calc 3 without calc 2? Yes, but I would strongly, strongly recommend against it.

 

[Vanadium 50]

Every school is a little different, so what might be good advice at one place is bad at another. That said, there are two possibilities: either you need to learn a particular topic's Calc 2 treatment before moving on to Calc 3, in which case skipping Calc 2 is a bad idea, or the material covered is completely independent, which means skipping Calc 2 is a bad idea because then you miss it entirely.

 

[captain math]

Hey guys,

thank you so much for your suggestions. I guess I will take Calc III and go over the mentioned chapters from Calc II in preparation. I hope I'll be able to make it.

Thanks again!

CM