what topics are covered in university (underGrad/Grad) calculus courses I thought calculus was one subject, in college I've seen:


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*Cal 1 - Single variable calculus 

*Cal 2 - Multi variable calculus 

*Cal 3 - ...

*Differential Eq Cal

*Vector Cal

*Nonlinear Dynamics cal (?)

*Diff Eqs in multiple variables linear/non-linear

*Real Analysis

*Complex Analysis

*Manifolds..?

*calculus of variations  (credit: dave)


what are these, are any of these same as above: 


*

*Elementary analysis

*Multivariable analysis

*Measure theory


My question is how all these relate to each other. What defines the word "Calculus" that many of these courses share in their title?
 A: There aren't any set number of calculus courses. This is something that will differ from university to university (or from high school to high school). Furthermore, what is Calculus 2 one place might not match exactly with what is Calculus 2 in another place.
Some places don't have Calculus at all, but will start with an introduction to real analysis. Some will say that calculus is really just a gentle introduction to real analysis. It deals with the same objects even though the specific questions studied might be completely different.
Many natural questions arise from calculus. If, for example, I know how to find derivatives, how to I go the other way and find a function given what the derivative is. This then becomes differential equations. These come in som many flavors that we have ordinary differential equations and partial differential equations. Real Analysis naturally leads to the question on how this works when the functions are complex instead of real. From here you go even go to the more general scenario where we are, for example, integration over sets with extra structure. This leads to measure theory.
Mathematics is often like that. When you have answered one question, then other natural question show up almost immediately. And this can lead to a whole new field. Going from real numbers to complex numbers changes so much that one can spend a whole careers are formed.
Loosely speaking Calculus is about derivatives (rates of change) and integrals (accumulated change?).
A: Actually this is incorrect based on where I live.
Based on my experience, Calc 1 is basically high school calc, (derivatives, curve sketching, limits)
Calc 2 is integration, series, sums, and more complex stuff like that
Calc 3 is MULTIVARIABLE, and its an extension of Calc 2, but in multivariable

I can't speak about the other courses
