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 Jul 28 revised Methods to solve differential equations added 755 characters in body Jul 28 revised Methods to solve differential equations added 755 characters in body Jul 28 answered Methods to solve differential equations Jul 28 comment Methods to solve differential equations I guess that we can do so, is guaranteed by the fundamental theorem of calculus involving Riemann Sums, showing that they are equivalent to the integral and that integration is inverse of differentiation. Jul 27 comment How to make notes when learning a new topic I have tried taking notes in LaTeX and unless you are taking lecture notes, which is mostly text and formatting, it is not really worth it. I never have been able to take lecture notes myself however. Though, some people have been apparently very successful. I also have a very bad handwriting, so I get what you are saying, but it (Live-TeXing) has been a big failure for me. mathoverflow.net/questions/12638/… Jul 27 comment Is there a bijection between mathematical structures and morphisms that preserve this structures forming a category? Just for clarification, since I am also new to the field. The OP is suggesting that we create a set $A$ of all the structures and set $B$ of all the morphisms and then show that there is a one-to-one correspondence between $A$ and $B$ right? Jul 26 revised Approximate solution for the root of a non-linear function added 10 characters in body Jul 26 revised Approximate solution for the root of a non-linear function Some clarifications. Jul 26 revised Approximate solution for the root of a non-linear function Added case for $w \ll 1$ Jul 26 answered Approximate solution for the root of a non-linear function Jul 26 revised How many decimal places are needed for incremental average calculation? added 8 characters in body Jul 26 revised How many decimal places are needed for incremental average calculation? corrected some typos Jul 25 comment Approximate solution for the root of a non-linear function Are you trying to solve some problem where you are trying to find out all points in time where a certain system satisfies a particular given property and hence you actually want the time closest to it because it is the next time the event happens or something similar? In this case the property satisfied at the time of happening of event is , $$e^{t_1} (g\cos(\omega t_1) + b) = e^{t_0} (g\cos(\omega t_0) + b)$$ Because, basically your problems seems to find out all such events given one particular event. Jul 25 comment Complete undergraduate bundle-pack You would be lucky to read all of them in next three years. Jul 25 awarded Teacher Jul 25 answered Complete undergraduate bundle-pack Jul 25 revised How many decimal places are needed for incremental average calculation? deleted 8 characters in body Jul 25 revised How many decimal places are needed for incremental average calculation? added 286 characters in body Jul 25 answered How many decimal places are needed for incremental average calculation? Jul 25 comment How many decimal places are needed for incremental average calculation? by $d$ decimal digits, you mean, $d$ significant figures right? It would also probably help if you can specify the the smallest allowed exponent, because then we can implement the formula in some special way to make use of the higher exponent available while still requiring only d significant digits For example, I would like the value of $n$ in the following expression and I guess the $d$ which you mention is as I have described. number = $a.a_{1}a_{2}...a_{d} \ \times \ 10^{-n}$