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Apr
6
answered Series solution to this differential equation
Apr
6
comment Series solution to this differential equation
Expand $e^{x^2}$ out using its power series (about zero). Then you can multiply out the first few terms of that series with the first few terms of the series its multiplying, and do the "usual" things from there to obtain the recurrence relation for the $a_n$...
Apr
5
comment Proving Exponential Convergence
Do you know Lyapunov's Theorem/Method for stability?
Mar
9
awarded  integration
Dec
13
awarded  Yearling
Nov
28
answered Linear Algebra: parametric line in 3d
Nov
26
answered Find $\int_0^{y^2}e^{-xy}dx$ using the Leibnitz integral
Nov
26
comment Find $\int_0^{y^2}e^{-xy}dx$ using the Leibnitz integral
The Leibniz integral rule is for differentiating an integral with respect to a variable that appears both in the limits of integration and the integrand. This is not the situation you have.
Nov
26
comment Can you solve $y'+x+e^y=0$ by series expansion?
$e^x$? yes. $e^y$? no.
Nov
26
revised Volume of sphere - order of integration
added 202 characters in body
Nov
26
answered Volume of sphere - order of integration
Sep
15
awarded  Revival
May
26
comment Fourier series coefficients proof
@Mark yes, every term in the series integrates out to be zero except for the one term where the summation index equals the (fixed) value of $m$, and in that case that term integrates to be $\pi/2$.
May
16
comment Intuition behind uniformly continuous functions
PS This might be helpful: youtube.com/watch?v=hXkQqCBLRp8
May
16
answered Intuition behind uniformly continuous functions
May
12
comment Linear Ordinary Differential Equation with Nonconstant Coefficients
Look for a power series solution...
Apr
10
comment Understanding the definition of a set with $C^k$ boundary and of the outward pointing normal vector field
How would you define the normal vector at the corners of the square? Think about what it means to be the normal vector there... And why a lack of $C^1$ is a problem...
Apr
10
comment Understanding the definition of a set with $C^k$ boundary and of the outward pointing normal vector field
How about $U$ the interior of a square? Then the boundary of $U$ is continuous, but not smooth ($C^1$) at the corners.
Apr
8
awarded  Enlightened
Apr
8
awarded  Nice Answer