Recent content by xaenn

Gotcha. It's essentially a calculus-like argument when it comes down to it. Thanks for your thoughts. :-)

Thanks for the responses. @pwsnafu: That's interesting - I wasn't familiar with the Generalized Mean Equality and that is a slick solution. Do you have any suggestions on how to make it more accessible and easy to think about for people with less math experience? @chingel: This was the way...

This is a fairly standard maximization problem in calculus, but I was wondering if anybody could help me come up with a nice geometric solution. It seems like it should be possible to make an argument based on symmetry, but I haven't quite been able to work it out yet. Note, I have already...

Hello all, I'm in the process of working on developing a course to prepare students for calculus. The emphasis is to build up students' conceptual mathematical thinking, particularly that related to the notion of the function. Recognizing that motivation is one of the biggest issues to...

Now that I've gotten a chance to pick up this book and go through it I just wanted to say it is a very nice introduction to numerical analysis. The presentation is clear and reading through the book has been extremely insightful. It's also piqued my interest to the point where I'd really like to...

Thank you very much for the explanation and image. Extremely insightful.

Or rather in an ideal world we can look at a function, break it into regions where it is positive and negative, and then consider them separately as signed areas. The only problem being that a priori you don't know where those areas are going to be. Thus, there is something of a jump between the...

You're probably right; I am sure this type of error probably is covered in the error analysis. I just found it curious because the thought that the trapezoidal rule would give you a shape other than a trapezoid never crossed my mind. This was pure laziness on my part. The original function I...

The trapezoidal rule for numerical integration is based on the idea that when we partition our larger interval into subintervals, we can approximate the area over each subinterval by calculating the area of the trapezoid formed by connecting the value of the function at the left and right...

Arildno, I think I probably need to be a little bit more clear with the question I am getting at. Your example function jumps between 1 and -1 at every natural number, so overall the amount of area we pick up can never be more than 1, but when we look at the improper integral it doesn't...

Thanks for clearing the LaTeX problem up for me. : )

I have some questions on the topic of improper integrals. I'm using Thomas' calculus 11th edition for reference, but I have a handful of other books providing me with the same information. When they are defining improper integrals, they work with the hypothesis that f(x) must be continuous on...

Many thanks for your explanation. It was extremely insightful, and illuminates the fact that my problem was an incorrect notion of work. Now that you have mentioned things such as the work kinetic energy theorem I do remember it from my days ago in physics. Thank you. So far I've been very...

Now I am clear on the fact that the energy came from the person lifting the box. However, I still have a bit of confusion, so perhaps someone can clarify a bit further. Letting the box be our system, we have two forces acting on it, gravity and the person lifting it up. According to the text...

Understood. I was thinking it was an issue of identifying the proper system, but I just wasn't being able to do so having not thought about classical mechanics for so long. Thanks for the quick response.