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I thought calculus was one subject, in college I've seen:

  • 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?

Muhammad Umer
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  • How your specific college subdivides/merges different subjects of math into different courses is pretty subjective, so it is difficult to answer your question since the number of courses is dependend on your personal situation. – M. Van Oct 16 '17 at 16:01
  • This highly depends on the college, so I vote to close this question. –  Oct 16 '17 at 16:01
  • So close to answering the question and it was closed – Thomas Oct 16 '17 at 16:05
  • Perhaps there is a better way to phrase your question, which will avoid the subjectivity of the current wording. Also, you might keep in mind that the word "calculus" has a very general meaning, even in mathematics: https://en.wikipedia.org/wiki/Calculus_(disambiguation) – Lee Mosher Oct 16 '17 at 16:05
  • My undergrad institution has at least 7 calculus 1 courses not even counting calc 2 or 3 or 4 (yes, some schools have a calc 4). Each department wanted a different selection of topics for their students. – Trevor Gunn Oct 16 '17 at 16:05
  • The answer to this question is not uniform, but that is very different to saying it's subjective. There are patterns in how these terms are used for courses, and it seems appropriate to ask about that. – Paul Oct 16 '17 at 16:07
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    To the OP, if you don't get the question re-opened, you might have better luck at the math education stack exchange. – Paul Oct 16 '17 at 16:08
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    There seems to be a reasonable question in here, but it's not "how many calculus courses are there?" So please change the title and edit your post accordingly. – Trevor Gunn Oct 16 '17 at 16:09
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    OP, I added a more reasonable question. If this is acceptable to you, maybe you can edit the title? – Thomas Oct 16 '17 at 16:10
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    For example, see: https://matheducators.stackexchange.com/questions/3939/naming-of-calculus-courses and – Paul Oct 16 '17 at 16:10
  • @Thomas can you still answer it – Muhammad Umer Oct 16 '17 at 16:27
  • @MuhammadUmer: Not when it is closed. It has to be reopened before anyone can write an answer. If it is reopened I will add my answer. – Thomas Oct 16 '17 at 16:37
  • i mean how many votes do you need to reopen – Muhammad Umer Oct 16 '17 at 16:52
  • @Math_QED i'm less interested in knowing what my college does, and more what topics there are, so i can self study even if i change major. I dont think my college is a good reference point to go on, they are hardly known for math and often dont even offer lot of math courses for years – Muhammad Umer Oct 16 '17 at 16:54
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    @MuhammadUmer You're question is 1 vote away from reopening. I can provide this vote but I will only do so after you change the title of the question to be more appropriate. For instance: "what topics are covered in university calculus courses?" or "what topics can be considered 'calculus'?" – Trevor Gunn Oct 16 '17 at 17:20
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    There's also calculus of variations (see here also). – Dave L. Renfro Oct 16 '17 at 20:59
  • done changing it – Muhammad Umer Oct 16 '17 at 21:05
  • i found an answer that sort of answers this https://math.stackexchange.com/questions/1734104/what-is-advanced-calculus/1734136 – Muhammad Umer Oct 17 '17 at 02:36

2 Answers2

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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?).

Thomas
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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

K Split X
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