Limits and the fundamental theorem came after this.
We used old school TI graphics calculators in the classroom. This was 15+ years ago so students today probably have better tools available (In Australia some schools give laptops to students nowso at least something like excel is available) we certainly had better then pencil and paper in the late 90's.
My first year university calculus course covered 2 years of high school math in about 5 weeks and moved on to things like Taylor series Laplace transforms etc. There were people who hadn't studied calculus at high school in the lectures but they were the minority. I'd imagine if this was their first exposure it would have been a struggle.
And I'm saying he doesn't much succeed at that. After the first few chapters, the content is either trivial or very similar to what you'd find in a textbook.
>As for the Wolfram Alpha comment, the idea is about "immersion".
You could be right, but it seems like a generous appraisal. It reads to me more like an attempt to brush over the fact that the student doesn't actually know any calculus yet.
If your intent is to teach that calculus can be performed intuitively, teach that - don't teach how you can phrase your question to get a computer to solve them.
No, he's not showing WolframAlpha as a mental shortcut to cover up deficiencies of not knowing calculus.
The point is to utilize it as a diagnostic tool to check the student's understanding of previous Ch 1 - 4. If the student understands the previous chapters' vocabulary and concepts, he "doublechecks" that understanding by seeing if he can "describe" problems to WolframAlpha. Again, the idea is to create a feedback loop for the self-directed learner.
Instead of using WolframAlpha, one could be shown how to use the TI-83 graphing calculator for the same purpose. However, since the student is likely reading Betterexplained on the web, he can just conveniently click over to wolframalpha.com and "check his calculus knowledge" there. As a bonus, WolframAlpha is easier to use, draws prettier graphs, and doesn't cost $100.
I think your criticism is misguided. His tutorial is obviously meant to make the introduction to the topic more accessible. He does that by using pictures and diagrams to build intuitions. He can do that because he extensively uses drawing tools to help the learner "visualize" what Calculus is about.
Compare that with typical calculus teacher with a whiteboard. Because the teacher's drawing skills are limited, he/she dives right into the delta-epsilon limit definition: lim h --> 0 for f(x+h)-f(h)/h
Yeah there's some hand drawing of tangent lines to converge on a "instantaneous change" but that's not enough for a lot of students to "get" Calculus. The symbolic notation is demonstrated more often than pictures. It therefore devolves into mindless "plug & chug" for the rest of the semester.
As for the Wolfram Alpha comment, the idea is about "immersion". There are other tools besides pencil-&-paper that also "do" Calculus and they can be used to verify self-study Q&A.
Likewise, if I teach Differential Equations to programmers, it's helpful if I "immerse" them into other tools to numerically solve them such as MS Excel, MATLAB, Wolfram Alpha, C/C++ code, etc.
His BetterExplained doesn't replace a rigorous Calculus textbook but it can help with the "aha!" moment to understand what the dry Calc textbook is trying to teach.