Hey guys, I am just looking for some online resources for solving the heat equation. So far I have looked at Paul's Online Math Notes:
http://tutorial.math.lamar.edu/Classes/DE/SolvingHeatEquation.aspx
But I don't feel very confident with the material yet. I would really like some more...
Thank you for responding.
I am looking specifically for examples of the algorithms as they were employed historically. If nobody can provide that, then I suppose I'll dig through the sources you listed.
Hello,
Analytic geometry has provided us with such profound tools for thinking that it is hard to imagine what thinking must have been like before we had such tools. Two particular developers of these tools are Pierre de Fermat and Renee Descartes in 17th century France.
I would like to...
Newton and Leibniz both had a method of differentiating. Newton had fluxions and Leibniz had something that resembles the modern derivative.
Historically, does anyone know how they went about calculating the derivative?
I am a 172. Formally tested five times and only one test was bold enough to put it at 172. The rest had me at 160+.I didn't have an education but I got a GED, scoring top percentile. I studied
for the SAT, did very well, and started my math at calculus 1. I've since aced the calculus series...
It doesn't matter where we start since inequality is reflexive. Showing a set A does not equal a set B is just as good as showing the set B does not equal the set A.
We were done when we found both sets and found the counter example, 0, in the second equation's solution set.
So, we can...
We are showing two sets (the solution sets) are not equal. It doesn't matter where we start.
I also addresses the issue of why the x he picked didn't satisfy the system of equations he constructed. This had the hypothesis of x^2-1=0.
x has graduated to playing a role in a system of equations once you start multiplying both sides of the first equation. Equation 1 still needs to be true.
I don't think there was a hypothesis imposter. The hypothesis was that x^2-1=0. Why would that change?
Starting with that hypothesis you know that x is 1 or -1. If you multiplied both sides of the equation by anything at all, then the equation would remain true. This is precisely because x is 1...
By hypothesis ##x^2-1=0##. We don't need that last implies.
The division is the cause of the problem.
##x(x^2-1)=0 \implies x = 0##
Is invalid. Really, it implies that ##x=0## or ##x=1## or ##x=-1##. But, it doesn't equal zero because that would not satisfy the condition in the hypothesis.
All x in the set of solutions, not in the set of real numbers. Then, all x means x=1 and x=-1. I'm sure that this is what he meant.
If we are changing the solution set of a polynomial, then we are changing the characteristic property of that polynomial. Hence, we would have a different...
These will all act as either tools in your proverbial toolbelt, examples to consider in further analysis, or a foundation for future insights.
Learning math is independent from where you go to school. Some schools will be more useful, but you can always learn on your own. As far as research...