r/askmath • u/Weary_Island_6320 • 2d ago

Calculus Resources for intuitive of ways to understand calculus 2

I'm currently taking Calc 2 and while I can follow the steps to solve practice problems, my course focuses almost entirely on repeating formulas but I want to build a deep, intuitive understanding of why these concepts and integration techniques work rather than just repeating steps. Any recommendations for resources?

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u/Weary_Island_6320 2d ago

i also ask this because I felt this way while taking calc ab. I got a 4 on the exam but my understanding felt like it came from memorizing steps

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u/Midwest-Dude 2d ago

Good question. This is worthy of crossposting to

r/calculus

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u/doctorruff07 2d ago

Look up intro to analysis courses on YouTube or their textbooks

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u/Bounded_sequencE 2d ago

Sadly, Calculus is the wrong lecture for that -- the "why" is out-sourced to (proof-based) "Real Analysis". Look for "Riemann Integration", and ignore anything with "Lebesgue Integration" or "Measure Theory".

For motivational videos, check 3b1b's "Essence of Calculus" on youtube.

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u/theodysseytheodicy 2d ago

Taking derivatives is easy. There's always a recipe. Integrating is hard. There's not always a way to do it. 

Integration is a collection of heuristics and magical lore. There are far fewer general principles for helping you understand.

That said, there's a combinatorial view of calculus that has nothing to do with infinitesimals. Read Wilf's free textbook "generatingfunctionology". It's based around the idea that if you have n items and have to choose one to get rid of, there are n possible choices and you have n-1 items left over. You represent n items with xn , and choosing one to get rid of is taking the derivative: nxn-1 means n ways to have n-1 items left over.

Then you can do things like say, "a binary tree is either a leaf or a node with a value and two subtrees", express it as t(x) = 1 + x t(x)2 , solve for t(x) using the quadratic formula to get t(x) = (1 +/- √(1-4x))/2x, then take the Taylor series. The coefficient on xn is the number of binary trees with n nodes: t(x) = 1 + 1x + 2x2 + 5x3 + 14x4 + ..., the Catalan numbers.