Our latest video is Refactoring Introductory Calculus, Part 1.
In computer programming, the word “refactoring” refers to taking a process apart and putting it back together with the components slightly shifted in order to make the result both easier to understand and use while simultaneously being more powerful. This is the first episode in a series about rethinking the way that calculus is taught and communicated in order to do the same thing – simplify the foundations while increasing the power of those foundations.
In this part, we will talk about how focusing on differentials instead of derivatives makes the process of calculus easier, giving a unified set of rules for single-variable, implicit, and multivariable derivatives. Additionally, the process given here removes the need for the chain rule, which simply follows naturally from the process rather than having to be some special rule.
Unfortunately, YouTube doesn’t allow arbitrary links, so we are linking all of the YouTube cards in the video to this post. Here are the links to the items discussed in the YouTube cards:
- Simplifying and Refactoring Introductory Calculus. This is the paper that serves as the basis for the video series.
- To see how this works with higher-order differentials, see the paper Extending the Algebraic Manipulation of Differentials.
Bartlett Publishing is proud to release two new books from author Jerry Bergman. Bergman is a prolific author and his previous book, Fossil Forensics, is one of out bestselling titles.
This fall, Bergman release two new titles – Poor Design: An Invalid Argument Against Intelligent Design and Useless Organs: The Rise and Fall of a Central Claim of Evolution. These two books are a stunning combination of physiology, philosophy, and natural history. They knit together the details of the systems of the human body together with the understanding of what they mean in the context of modern claims about the nature of humanity.
Bergman skillfully shows that the things that we used to think were junk (or poorly designed) were, to a large extent, a testimony to our ignorance about those systems rather than evidence of their poor design or lack of function. Biology is best understood in the context of well-organized systems, and these books show why this conception is better than the alternatives.
These are perfect books to read on their own. However, they should also be considered for use as supplemental material for homeschool biology and anatomy courses.
We are getting serious about our YouTube channel, youtube.com/BPLearningTV. We just uploaded the first video in a long time on the Hyperreal Number System! Check out the video, and don’t forget to like and subscribe to the channel.