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The problems in Spivak are pretty good I think - they'll show if you can do maths or not. Some also have answers (and an answer book for the rest), so there's
by hyperpallium2 6y ago
The problems in Spivak are pretty good I think - they'll show if you can do maths or not.
Some also have answers (and an answer book for the rest), so there's examples of explaining what was done, for harder ones. The explanations are sometimes too concise, but at least it gives some guide for how you can explain your answers.
At a much easier level, Khan Academy videos mostly are explaining how a specific problem was solved - another resource.
- swiley 6y agoMeh. Everyone pushes their favorite calculus book but I think better is to just try to push yourself to gain an intuition for your subject. Try to visualize what it is the text is saying, try to apply the problem etc. When I took calculus there were three things that really helped me with this: 1) A study partner that's competitive. when you have an intuition you're more likely to get the correct answer first because you can check what's going on quickly without having to recalculate things. Also when they get stuck you'll be expected to explain how you figured it out. Studying with someone like this will force you to grow an intuition. 2) Writing programs that use what you've learned. At least for me this helped a lot. I learned to program before I learned any interesting math so being able to rewrite what are often implicit ideas in an explicit language can really help you think things through. Like many people here I gained an intuition for integration early on by writing physics engines for games. 3) Just meditate on the ideas.