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seen Aug 23 at 19:51

May
23
comment Using Integration By Parts results in 0 = 1
There is no mistake, and it does not prove 0 = 1. It proves only that 0 = 1 + $C$ for some constant $C$. An indefinite integral always has a constant of integration to be taken into account. You may have noticed in Calculus 2 that you come up with the exact same kind of result when you integrate by parts the expression $\ln (x+1)$ directly without intermediate $u$-substition vs. doing it with intermediate $u$-substition, as another example.
May
1
answered Linear Algebra Confusion!
Mar
20
awarded  Yearling
Dec
5
comment Solving Partial differential equation , distinguishing the meaning of boundary condition and Initial condition.
Yes, boundary basically is like the external state which can be measured without entering the object being considered. In a way, the "future" is like the internal state of the object which we cannot penetrate. So the initial condition when time is 0 (the present time), is like the boundary of the object that represents the future. So initial conditions are very closely related to boundary conditions. The initial condition when time equals zero is simply the boundary condition at the edge of the object that represents the future.
Dec
4
answered Solving Partial differential equation , distinguishing the meaning of boundary condition and Initial condition.
May
14
awarded  Caucus
May
10
answered Is mathematics one big tautology?
May
3
awarded  Supporter
Apr
30
comment Truth Value of Multiple Quantifiers
@user794954 your first statement is false as I said, and your example shows why it is wrong. Your second statement is true and is not equivalent to the first.
Apr
29
answered Truth Value of Multiple Quantifiers
Apr
26
answered Logarithm rules, which one has priority? $\ln2e^{2x}$
Apr
4
comment Studying for the Putnam Exam
You may do that if you like. I did not know there were official solutions now available online.
Apr
3
awarded  Teacher
Apr
3
comment Studying for the Putnam Exam
I totally agree that the proof writing classes and the resulting understanding of making a logical argument starting from premises while defining every item along the way, is more valuable than just knowing how to do calculus!!
Apr
3
answered Studying for the Putnam Exam