Integration of the knowledge of a derivative

On the web it may be more difficult to integrate the equations and graphs for a specific study. With the use of my Zim wiki, which is now powered by python, it includes an equation editor for LaTeX images, links to resources like videos, cross reference as well as the integration of GnuPlot as a standard feature. In this case I can take the equation from a recitation example, create the LaTex representation, plot the example in GnuPlot and have it included as source, and with the addition of my own python extension, perform an analysis that produces the desired solution, which is in this case the derivative of the given equation by the rules. Which can then be analyzed and present the information such as zero crossing, convergence, continuity and even run a Monte Carlo against the function to identify any unusual aspects that might not be immediately obvious.

In this case I am taking the 87 recitation videos for 18.01 single variable calculus and creating a composite that integrates as well as differentiates the information to a product that serves to enhance understanding as well as improve representation and programming skills. I plan to produce an OpenGL output using my chalkboard program that integrates the GnuPlot and LaTeX data with the audio in such a form that it is a video constructed from the generated voice based on a transcript and a model character which is animated to do voice under. It produces a script with scene descriptions as well as dialogue and stage movements of the characters in XML that are translated to OpenGL commands and are then in a state such that they can immediately be converted to WebGL.

The bandwidth of a script with dialogue is several K as opposed to several M for a frame by frame video which is immutable in its form and cannot be re-purposed for any other lecture or presentation. It seems there is a web application that does this and perhaps I will investigate that. It seems that it would be easier and more advantageous in the long run to do the character conversion locally. I can change the scene and characters and voices with a single line of XML and so I can make it be in the jungle with the creature from Alien as the professor and the dialogue from any source. It would seem that though many methods push for higher and higher bandwidths and less control of the information, this would allow a great deal more freedom and more flexibility.