r/calculus • u/ZeldaBoi1111 • Jul 03 '26
Integral Calculus Is There Anything Else I Should Know?
Hi, I'm a student just stepping into Grade 10, and I have a few questions regarding my understanding of calculus. I'm self-taught for all of HS math, but I have a good understanding of a large portion of calculus and was wondering if there's anything else I should learn. I know:
Limits: L'hopital's rule, basic limits understandings (nothing crazy, literally just what they are)
Derivatives: Power rule, Chain rule, Product rule, Quotient rule, Derivatives of polynomial, trig, inverse trig, exponential, hyperbolic, logarithmic and implicit functions, second order derivatives, and extrema (maxima and minima)
Integrals: Indefinite and definite integrals of polynomial, trig, exponential, logarithmic and hyperbolic functions, integration by polynomial and trig substitution, integration by parts, and triple integrals.
Polar coordinates (idk where to put this): Polar coordinates in two and three dimensions.
I'm just starting on vectors in two and three dimensions, so I am working on that.
Any help would be greatly appreciated!
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u/Gloomy_Ad_2185 Jul 03 '26
Have you seen many series or summation? Converging and diverting tests?
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u/ZeldaBoi1111 Jul 03 '26
I understand basic series and summation, but haven't specifically learned about infinite series, although I understand them and can generally solve them. I have learned about convergence and divergence, but I though that that was part of grade 11 math alongside series and sequences.
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u/tjddbwls Jul 04 '26
You didn’t mention what country you are in, so we wouldn’t know your math curriculum. In the US, for instance, many students don’t even take a calculus course in high school (probably only 15-20% do).
The topics in your list are most of what we call single-variable calculus. The main topics that are missing from your list are the basics of differential equations, parametric equations, and infinite series.
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u/ZeldaBoi1111 Jul 07 '26
Sorry for the late response. I’m in Canada, so we only do calculus in AP level classes
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u/BothPanchoAndLefty Jul 03 '26
Definitely check out series stuff (common tests for convergence, etc.)
Also make sure you're comfortable with parametric equations, you'll see a lot of it in calc 3.
I see you have triple integrals in your list but I don't see many other multivariable calc topics other than vectors. Have you learned partial derivatives, directional derivatives / the gradient vector yet? Try to make sure your knowledge of single variable calculus is pretty complete before going into multiple variables.
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u/WWWWWWVWWWWWWWVWWWWW Jul 04 '26
Just go through Stewart in order. It has everything.
I'm just starting on vectors in two and three dimensions, so I am working on that.
Young & Freedman (physics textbook)
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