What is Calculus IV? don't understand my university's math offerings

[Raiv11]

So the independent research I've done indicates that the usual calculus sequence is Calc I-III, where III covers lots of multivariable stuff. My program requires me to take two calculus courses beyond first year, which sounds like more than usual. My suspicion is that our "Calc III" doesn't cover everything that Calc III usually does, and our Calc IV covers a little bit more and some other material.

I know I need both courses if I want Math on my degree (which I might) but I don't really understand what's going with them and I was hoping I could get some advice on what to expect or if this "Calc IV" class is worthwhile.

Intermediate Calculus I:

Topics include review of paramatric equations polar coordinates, conic sections, coordinate systems and vectors, dot product and cross product, vector functions, derivatives and integrals of vector functions, arc length and curvature, functions of several variables and partial derivatives, directional and double and triple integrals.


Intermediate Calculus II:

Topics include multiple integrals and changes of variables, and vector calculus, with an emphasis on Green's and Stokes' theorems. The course also includes an introduction to second order ordinary differential equations.


If it helps, the latter course appears to use Ch. 15 onwards of Stewart, and that's the one I'm wondering about. Does it sound like this "Calc IV" class is of any use? Does it extend beyond the usual calculus sequence that I've heard so much reference to? Any insight/advice would be greatly appreciated.

[qwertyater]

At my school (McMaster) we have calc 1 and 2 in first year.
Then in 2nd year there is calc 3, which covers multiple integrals, vector calc, etc
And then there is advanced calc 1 and 2 which covers the above in more detail and also covers a few more topics.

Also here, you are supposed to take advanced calc 1 and 2 before taking any type of Analysis course.

So if you're wondering if you should take intermediate calc 2, do so if you need it to take the upper year math courses like Real Analysis.

[Raiv11]

My school has "Introductory Analysis" (2nd-year course) and "Intermediate Analysis" (3rd-year course that would last all year) and that's the extent of everything offered relating to analysis. I'm planning to do all three semesters of Analysis and all they want is linear algebra (proof-based) for it. The advanced calculus content is built into the Intro Analysis course, I think, which is why it's not required.

[moneyandcredit]

Let me guess: your school is on a quarter system. If that's the case, it's normal to have Calc I-IV, plus Intro to Linear (Matrix) Algebra, plus Intro to Differential Equations. This makes a total of 6 courses spanning two years, covering everything found in a semester-system school.

If I'm correct about this, then you should definitely take the Calculus IV class plus the lower-division Linear and Differentials courses. Unless you're smarter than I am and can handle the hardcore proof-based approach to advanced multivariable calculus techniques as your first exposure.

[Raiv11]

I think my school is on a semester system, if that means what I think it does. Our Fall and Winter terms run from Sept-Dec and Jan-Apr. Calc I-IV each lasts one term (which takes a full two years of math); LA is two courses, usually done in 2nd year. And then Intro ODE and Analysis are separate courses on top of that, which each take one term. Does this make any sense?

[moneyandcredit]

Yes, that makes sense. Had I read your previous post more clearly I would have noticed you made a passing reference to your school's semester system.

[Adamah]

I commonly hear people refer to Differential Equations as "Calc IV". That might be it.

[moneyandcredit]

I found a few Canadian universities with a Calculus IV class. Looks like it usually discusses some of the topics that a few professors leave out of Calculus III due to time constraints... as in they're usually on the syllabus for Calc III but maybe enough professors at that school never got that far so they just made a fourth semester of Calculus.

[peter mouganie]

I have a couple of friends in universities with calc 3 and calc 4

Basically calc III in standard universities usually covers everything.

However some universities break it up into Calc III and Calc IV usually to focus in more detail on the topics.

Calc IV deals with the last 2 or chapters i think of Thomas's calculus. It dealds with double integrals, triple integrals, Stoke's thoerem, Divergence theorem, flux, flow, etc... Pretty much a civil engineer's worst nightmare because he will be using all concepts in great detail later on

[moneyandcredit]

Having a fourth semester of basic calculus seems like a good idea, since it allows more time to be dedicated to the aforementioned topics. I wish I had that opportunity. However, it could also be said that professors and students should be working harder to get it done in the traditional three semesters.