Recent content by Husaaved

I am using the text by Farlow to study elementary methods of solving PDEs, and there is a point in his illustration of separation of variables where I am not seeing something. I am clear on everything that comes after and before this point, but after having returned to a certain step a few times...

So, when I change the indices, I'm getting: \sum_{n=1}^\infty na_nx^{n-1} = \sum_{n=1}^\infty 2a_{n+1}x^{n+2} or \sum_{n=0}^\infty (n+1)a_{n+1}x^{n} = \sum_{n=0}^\infty 2a_{n}x^{n+1} -- which doesn't quite lead me to the na_n = 2a_{n-2} that Boas ends up with. I have solved these...

Oops, miss post

Working through Mathematical Methods in the Physical Sciences by Boas, on the chapter on Series Solutions of Differential Equations, Boas works the example: y' = 2xy Boas differentiates the series representation of y yielding y', substitutes both into the original equation, and expands...

Ahhh, I hadn't noticed. Thank you -- I'll know to be more mindful with that. I actually really love the text! I'm taking all three classes as separate courses, and for multivariable we are using Stewart, for ODEs we're using An Introduction to Ordinary Differential Equations by Earl...

Nothing -- I actually agree with you. Clarifying what physics actually is to younger students is ultimately beneficial. In fact I feel many people don't go into physics I believe because they equate it with the buzzwords, which are seen as abstractions with little bearing or relevance to...

Hello, I realize this reply is very late -- sorry! I called it "varition of constants" because that is what it is called in one of the books I am using, "Multivariable Calculus, Linear Algebra, and Differential Equations" second edition by Stanley L. Grossman: 11.11 Nonhomogenous Equations...

I feel like making active efforts to temper the excitement that high school kids or even more mature students have about physics is a great way to kill their interest and enthusiasm completely. Like, for that matter then you should go around telling undergrad chemistry students that no, it's not...

Hello, I am in an introductory undergraduate course on ODEs, currently on the method of variation of constants to solve nonhomogenous equations. I am noticing that with many of these problems, when solving for constants after plugging in my guessed values for y I end up with enormous...

People with mental illness are far more likely to be the victims of violence than they are to be the perpetrators of it.

Thank you so much, I wasn't expecting such a detailed or helpful response.

This isn't really a homework question, more just something I noticed while evaluating an integral and was curious about: At this stage, I was able to simplify the expression before solving for the integral algebraically (since the second iteration yielded the original integral the right...

The problem is to a.) solve for the slope m of the hypotenuse of the right triangle indicated by the shaded area, and b.) solve for the length of the hypotenuse, if possible. I made a mistake in transcribing the problem onto paper, the line of course extends indefinitely but the shaded area and...

I'm not entirely sure if this belongs in homework or elsewhere -- I'm self-teaching working through a basic calculus text, so it's not homework per se. In any case it's a simple differentiation problem wherein I am supposed to differentiate: f(x) = x(3x-9)^3 f'(x) = 3x(3)(3x-9)^2 Applying...

Thank you very much for your response, sorry for the typo.