Friday, 03 June 2005, 18:22:57 EDT
Last semester I took Calculus I. The course covered differential calculus and finished off leading in to integral calculus. By the end of the semester I was fried and couldn't handle any more so I didn't really get the integral stuff that we talked about. Well, I have had three weeks off and am starting in with Calculus II. This course begins with the very next section in the book where we left off in Calculus I. So, I have been working on catching up, I only missed two sections, over the past couple of days. The section that I stopped working on last semester had to do with Reimann Sums. Today, I finally figured out how to do them; it turns out that I was skipping one simple thing.
Let's look at the integral . This particular integral could be solved in the following manner:
That is the correct result but it is not the correct way to achieve it. If you were to solve the integral in that manner you would end up with a result of "2" when the true result is "3". The correct way to solve the problem is like so:
I was going crazy trying to figure out what I was doing wrong. Now that I have it figured out it isn't really that hard. Now I can get caught up rather quickly.
While I am on the subject, creating those images is more difficult than the math work in them. I can't find a single good, free, WYSIWYG equation editor. At least not one that would have made creating those images simple. LaTeX Equation Editor is excellent for the inline equations that are in this post but sucks really badly when it comes to the multi-line solutions. I had to use Math from the OpenOffice.org suite to type the equations. Then I had to save them as PDFs, convert the PDFs to PNGs with Automator, and finally crop the equations out of the images and resize them with an image editor. Once I figured out how to use Math it was quite simple; I wouldn't want to use it all the time but the application does get the job done. If you want the sxm files to see how to use the application I can email them to you.
I did some searching around to determine how difficult it would be to render LaTeX in to images on the fly. It wouldn't be too difficult to do but it would take me a bit more time to initially implement than the time I spent on this today. I think that I will do that at some point though. I have enjoyed creating this post and would like to be able to easily create more like it. If I were able to just type up the LaTeX in Equation Editor, to validate it, and then copy & paste it in my post editor that would be really nice. Why LaTeX? It has excellent math rendering abilities.