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Sophomore Graduate Student in Mathematics


Jul
31
comment Limit of binomial coefficient
@J.M., Thanks for the info.
Jul
31
comment Limit of binomial coefficient
@J.M. : He is using the notation for combination, so probably he means a non-negative integer?
Jul
30
comment Approximated Laplace transform of a non-linear system
@mmm: en.wikipedia.org/wiki/…
Jul
30
comment Approximated Laplace transform of a non-linear system
$\dot{\omega}(t) \approx \alpha_0 \omega(t) + \beta_0 i(t)$ is a valid assumption for only $t \approx 0$ since $\dot{\omega}(t)$ is largely negative and very large and stays like that until $\omega\left(t\right)$ is very small. So, that is one source of error.
Jul
30
comment Approximated Laplace transform of a non-linear system
If you can give me approximate regions (in terms of actual values of $\omega$ and $i$ in which you want the solution, it might be better/easier to solve. I can solve it most probably even if you are able to provide the value of $\omega(t)$ as $t \rightarrow \infty$.
Jul
29
comment Open mapping of the unit ball into itself
Ohh, right. Sorry. I missed the open part. So careless of me.
Jul
29
comment How many math classes should I take a year and of what sort?
@MichaelChen: Can you please elaborate the differences between masters level and PhD level algebra/analysis/topology courses? Do you have any extra information about them? I have been searching for information and I only see graduate and undergraduate courses, no such other distinction. Do you mean specialized algebra courses, like commutative algebra or similar?
Jul
28
revised Methods to solve differential equations
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Jul
28
revised Methods to solve differential equations
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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
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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?
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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 , \begin{equation} e^{t_1} (g\cos(\omega t_1) + b) = e^{t_0} (g\cos(\omega t_0) + b) \end{equation} Because, basically your problems seems to find out all such events given one particular event.