Brian Vandenberg
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 Oct17 comment Self Study in Dynamical Systems Unfortunately, the link you've provided appears to be broken. Aug11 comment Recommendation for a book and other material on dynamical systems I just ran across this course, for others who are interested: youtube.com/watch?v=mkfU9zVNGkQ&feature=relmfu Jun28 comment Online tools for doing symbolic mathematics +1, this looks like an interesting tool. Jun27 comment Online tools for doing symbolic mathematics It's as though everything lately has been telling me to learn Python. +1 for answering with precisely what I asked for: a web-based app that provides symbolic manipulation that isn't limited to one-liners. Jun22 comment Using differentials @Noteventhetutorknows - The fractional notation helps give the notion of rates, but it also gives the impression you can just do normal algebraic manipulations on them -- which is definitely not true. It can be done, as Americo Tavares points out, but it must be done very carefully and rigorously. Jun22 comment Using differentials +1 because it has the potential to generate answers to help explain proper use of differentials. Jun22 comment Using differentials @Theo - That's fine. What affect does \$\$ have? Jun22 comment Using differentials @Noteventhetutorknows - re: dubiousness, I was specifically referring to the homogeneous equation I wrote, but what you wrote is fraught with what I would consider to be inappropriate manipulations. The chain rule gives: $\frac{dy}{dx} = \frac{dy}{dt}\frac{dt}{dx}$. Nothing about the chain rule says it's safe or valid to swap denominators as though $\frac{dy}{dt}$ is a simple fraction. Jun22 comment Using differentials Agreed. When I took my ODE class I just went with it, but as I went back and worked through some of that material years later it occurred to me that the homogeneous equation above is actually a partial differential equation in disguise, of sorts -- hence my addendum with $\frac{dy}{dt}$ (etc). Adding $t$ explicitly seemed to make it easier to 'guess' the solution for those problems. May16 comment Convolution & DFTs: How much zero padding is necessary to avoid circular convolution? @joriki - Very good point, thank you. If you want to provide the correct answer and that note as part of your answer, I'll accept it. May16 comment Convolution & DFTs: How much zero padding is necessary to avoid circular convolution? Scratch that. The answer is $2N - 1$ along each dimension. See the following: cnx.org/content/m10963/latest Apr21 comment Is this a positive semi- definite matrix The OP didn't ask about 2x2 matrices. Apr21 comment The 9 Billion Names of God Although this is an interesting experience, the format of your question is very open-ended. There's no way anyone can give a 'right' answer, and often no answer is selected to be accepted for open-ended questions. Apr20 comment Maximization of Two Areas — Calculus 1 I'm a little unsure how to pull this off without another constraint. It seems like a circle is the most efficient shape in terms of containing the most area, so any expression you come up with would force the square's perimeter to zero and give you a circle with circumference = 10 meters. Apr19 comment how do you solve $y''+2y'-3y=0$? @night - That notation is not at all uncommon. I've encountered it in 3 texts for undergrad study, and it's one of the most useful techniques discussed in the differential equations "Problem Solvers" book -- with plenty of examples given, albeit more awkwardly typed. Apr12 comment Genetic Algorithms The next step will be to choose something you want to encode for the algorithm to work with. The two most obvious (only?) things you can model (or use to model) are actions to take within the game, and current/previous game state/actions. One way to handle it could be to use your genetic sequence to weight how important information is about current/previous game states and previous moves, then use some type of weighted sum to determine future moves. The paper you linked to probably describes the encoding they used. Apr8 comment Rules of Division @Bill - Well put. Apr8 comment Rules of Division @Bill - No. You made a good argument for a more general treatment of the topic. I'm arguing that there should be a "simplified" treatment as well. My point about the math jargon was to make the point that it doesn't need to be only readable by someone who has a desire to invest themselves in math enough to understand the more general/rigorous treatment. Apr8 comment Rules of Division @Bill - That's an excellent point, but in this case the OP needed it for the GRE. One of the more frustrating things for me 'growing up' in math was trying to digest material in Mathworld and Wikipedia math entries -- mostly because they were loaded with math jargon I was unfamiliar with. If someone's studying for the GRE, they shouldn't have to know a lot of math jargon just to learn a couple of divisibility tests. Apr8 comment Rules of Division @Bill - An answer is an answer. If original content was the requirement, most answers would be illegitimate because in most cases people would be quoting from, or regurgitating material from another source -- often without credit given.