<p>I'm currently a student Canada and I'm considering transferring to an American school next year for engineering. What's all this talk about Calculus I, II, III, IV, etc? Does the states have a unified calculus curriculum for all the universities? In Canada, our universities go by their own course codes and it's very different. Can anyone tell me what does each course teach? I reckon Calculus I is differential calculus and basic integration, II is integration and series, III is vector and multivar, IV is ODEs?</p>
<p>If so, I've taken IB Math HL in high school which I guess covers Calculus I and II. And I've also taken vector and multivariable calculus in first year university as well as linear algebra. Except, I haven't been formally taught series in university yet even though I'm already past vector and multivariable calc. I've been taught it in high school but I've forgotten a large portion of it. Will I be in a big disadvantage if I transfer to somewhere in the States and am expected to know series?</p>
<p>I have never heard of anywhere having a Calc IV as part of their calculus sequence. Some places have a course called advanced calculus or maybe some call it Calc IV, but I have never heard of it being required except in a few isolated cases. Generally, Calc I, II, and III are required along with Differential Equations (only covers ODEs) and Linear Algebra. It seems that is the trend at most places. Some require that advanced calculus, some require PDEs (rarely have I heard of this) and some don’t require Linear Algebra.</p>
<p>Series vary in importance with whatever major you happen to be pursuing. They sometimes get important in the advanced classes, though, especially the Taylor series and binomial expansion “series.”</p>
<p>People on CC and elsewhere commonly refer to Calc IV as being DiffEq. It’s actual name isn’t “Calc IV”, like the others with numeric sequential names.</p>
<p>If your school is on quarters instead of semesters, there will be a Calculus IV. The material is as follows:</p>
<p>Calculus I: Limits, Derivatives, Sequences and all that mess
Calculus II: Integration, Integration by parts and all that mess
Calculus III: Vectors, Gradients and all that mess
Calculus IV: Double, Triple Integrals, Green’s Theorem and all that mess</p>
<p>Basically the quarter system spreads 3 semesters of Calculus over 4 quarters. When I was an undergrad at Michigan State, we were on quarters. That has since changed. I think only Ohio State is the only Big-10 school on quarters (tri-mesters).</p>
<p>Calculus I: Limits, Derivatives, and all that mess
Calculus II: Integration, Integration by parts,sequences & series and all that mess
Calculus III: Vectors, Gradients and all that mess, Double, Triple Integrals, Green’s Theorem and all that mess
Calculus IV: Differential equations</p>
<p>" Some places have a course called advanced calculus or maybe some call it Calc IV, but I have never heard of it being required except in a few isolated cases."</p>
<p>Generally Calc 4 is DiffEQ. I don’t know about everywhere, but Michigan calls Real Analysis “Advanced Calculus.”</p>
<p>My school on the semester system does:
Calc I: Limits, derivative, sequences, and other crap
Calc II: Integration, and all the different ways to do it
Differential Equations:ODEs only
Calc III: vectors, gradients, double and triple integrals, greens and stokes theorems</p>
<p>The school I am at now does it like this:
Calc I: Regular intro calc, derivatives, limits, integrals, etc. A 3 or a 4 on an AP calc AB exam will get you out of this.
Calc II: Sequences, series, advanced derivatives, integrals
Calc III: Differential equations & Linear Algebra
Calc IV: Multivariable / 3D calc.</p>
<p>However, it seems that the more universal structure and how the school I transferred from did it:
Calc I: same as above
Calc II: same as above
Calc III: Multivariable, greens, stokes, etc. (my school did multivariable in 3 months and then 1 month of an entire DiffEQ course for the semester and that counted as “Calc III”.)
Linear Algebra</p>
<p>to the OP it’s hard to say if you will be at a big disadvantage or not. A lot of what I get from my engineering peers is that if we need to know an uncommon calculus concept for something in a class everyone pretty much needs a refresher.</p>
<p>Every school is different:
General seems to be:
I- Derivatives + applications and Integration
II- Integration applications, parametric equations and polar coordinates, sequences
III- Multivariable</p>
<p>My school is on the quarter system and we do things in a bizarre order:
I- Differentiation and parametric equations
II- Integration and a couple weeks of Diff Eqs
III- Basics of multivariable (partial derivatives, vectors, 3d space, double integrals, polar coordinates) and series.
IV: The theorems of multivariable, triple integrals, some other loose ends.</p>
<p>It works out well because most majors (including engineering) require only Calc I-III since IV is really just tying some loose ends and so most have their calculus requirement done within the first year.</p>