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I've studied basic math a very long time ago and would like to start over. I remember studying derivatives, but never really understood what rates of change were. I would like to know calculus, differential equations, dynamical systems. What information should I begin studying? should I know in depth about ratios, proportions, rates of change? I'm not very confident on these, especially rates of change. Should I begin by refreshing over this material? can anyone please also recommend any introductory material regarding these that I could start from. Thank you.

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    $\begingroup$ While trig isn't required for calculus (I never took a class on it and ignored it until I got to complex analysis and could easily derive the results) many textbooks assume it as background and thus make examples rely on it. If you plan to self study, that might be a place to seriously brush up your skills $\endgroup$ Commented Jan 19, 2019 at 21:42
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    $\begingroup$ If you want to seriously study dynamical systems and diff Eqs, I'd focus at least somewhat on learning how to prove things and read proofs. You may not need to do this if you have only applications in mind, but it can definitely help deepen understanding $\endgroup$ Commented Jan 19, 2019 at 21:46
  • $\begingroup$ I have self taught how to read and write proofs so I am comfortable with that. I've been reading through some calculus books and get confused on rates of change and what they are. I don't know why I get a mental block with this elementary topic and would like to change this asap. I have been reading up on modelling using differential equations and would like to know the meaning and understand the concepts $\endgroup$
    – user636392
    Commented Jan 19, 2019 at 21:55
  • $\begingroup$ Duplicates math.stackexchange.com/q/466926. $\endgroup$
    – user851668
    Commented Jul 2, 2021 at 7:01

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A strong foundation in algebra Is very important, as most if not all of calculus relies on the idea of a function, something that is covered very in-depth in algebra 1 and 2. For example, the pre-calculus course at my school covers: polynomials, sketching graphs, trigonometry, and exponential and logarithmic functions. Another topic that I would recommend covering but isn't necessary is limits, as they are the foundation to all of calculus, but most textbooks and courses spend the first few chapters discussing them.

One great textbook I found useful was this Calc 1 textbook. However, learning math from just a textbook can be difficult, especially Calculus, because it introduces so many new subjects, so you might find 3Blue1Brown's Essence of Calculus youtube videos helpful.

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