Undergrad Difference Analysis and Calculus

[ItsTheSebbe]

I'm a bit torn on what the difference between analysis and calculus is, I read somewhere that calculus is pretty much analysis without proofs? Either way, I see a lot of people mention problems being on calculus 1 or 2 level. I have finished Analysis 1 and 2 and covered stuff like (series, ODE, multivariable functions, double integrals, Fourier series/transforms, Lagrange multipliers, etc), is that comparable to the calculus 1 and 2 I see mentioned so often?

 

[fresh_42]

I suspect that English speaking people may see it differently, but in my language, calculus is used in a completely different manner and is a general term for a framework, in which calculations can be done, such as logic, set theory or arithmetic. We call analysis, what in English is called calculus. So I wouldn't spent too much thoughts on what might be the difference.

 

[mathman]

There are no precise rules to define these terms. Usually at a college level, calculus is used for the beginning course (derivatives, integrals), while analysis refers to more advanced material based on calculus.

 

[sudhirking]

This is an opinionated response. I would say Analysis re-examines those things conceived in calculus that had not the precise notion of "infinitesimals" which is ultimately found in limits. If we hear the subjects "calculus" we immediately think of Newton, Leibniz, and other pioneers and we think of their naive notions of taking limits and of infinitesimals. The departure from the naeivity of this field to something mathematically kosher, vigorous, is I think the departure of calling something calculus and calling something analysis.

Take Complex Analysis for example. It comes out of a simple yet profound phenomena that occurs with complex numbers and functions of complex numbers into complex numbers. And that is degeneracy or multi-valuedness of complex functions. From this quality comes an entirely new kind of calculus. Then if we use the actual vigorous definition of limits used in calculus, this becomes less "naive" complex calculus and more "proper" complex calculus. It becomes complex analysis.

So those terms I feel are basically interchangeable depending on the depth of the inner working of the calculus one is going towards.

 

[lavinia]

Personally I think of calculus as the study of differentiable functions and analysis as the study of measurable functions. You might separate probability theory as a third subject since it relies on the idea of independence while the rest of analysis does not.

 

[alabi qoosim]

5n+1 +7n+1

5n- 7n
solve this mathematical expression at limit tends to infinity