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This was the book my 1st sem. calculus class used in 1986, at UW-Madison (where the link is hosted and where the author presumably teaches). I remember it as p

This was the book my 1st sem. calculus class used in 1986, at UW-Madison (where the link is hosted and where the author presumably teaches). I remember it as providing a fairly gentle introduction to differentiation, providing a stepping-stone to more traditional notions of limits later on. I was just thinking the other day about how enjoyable I found learning calculus, compared to what others tend to report. Perhaps this book was part of the story -- very cool that it is being provided free of charge now!

mcguire 5y ago
In roughly 1987-1988, I took the required 2 semesters of calculus at UT Austin. It actually took me 4 semesters, for a number of reasons including that I was seriously unprepared for calculus. But the worst part of the experience was the method of starting with epsilon/delta and limits, to "explain" what was going on, and then throwing that away to get on with solving problems using differentials and integrals. The lectures almost universally took the form of the professor going through a proof of the technique in question and then assigning a set of problems from the text.
- bachmeier 5y ago
  I had to retake the first calculus class. Didn't have much to do with the difficulty of the material, but rather a professor doing things that would get him pulled from the classroom in 2021. Just one of the many things he'd do is call on someone to answer a question during the class. If he didn't like the answer he'd tell them they were lazy or that they should quit college.
- dkarl 5y ago
  > But the worst part of the experience was the method of starting with epsilon/delta and limits, to "explain" what was going on, and then throwing that away to get on with solving problems using differentials and integrals I guess that was pretty normal once upon a time? I remember that was how my calculus textbooks did it. First pictures to develop some visual intuition, then a gentle foray into how to make the intuitions more rigorous using limits, sequences, and series, and then techniques for solving certain differentiation and integration problems. It makes sense to me; it shows that the techniques are based in math and not in magic, and it lays the groundwork to introduce Taylor series later. It also foreshadows the kinds of proofs that students might do in real analysis if they decide to pursue an engineering or physical science major. I guess every math class could be very different if you knew it was the last math class that students would take, but you don't know that, and it's problematic to separate students according to which ones will study the material further before they're even exposed to it. If a student takes a class and unexpectedly finds they want (or need) to take further classes in the area, they don't want to be find out later that, "Oh, sorry, we didn't think you would pursue this subject, so we gave you the version of the class that didn't prepare you for the next one."

mcguire 5y ago

In roughly 1987-1988, I took the required 2 semesters of calculus at UT Austin. It actually took me 4 semesters, for a number of reasons including that I was seriously unprepared for calculus. But the worst part of the experience was the method of starting with epsilon/delta and limits, to "explain" what was going on, and then throwing that away to get on with solving problems using differentials and integrals. The lectures almost universally took the form of the professor going through a proof of the technique in question and then assigning a set of problems from the text.

bachmeier 5y ago
I had to retake the first calculus class. Didn't have much to do with the difficulty of the material, but rather a professor doing things that would get him pulled from the classroom in 2021. Just one of the many things he'd do is call on someone to answer a question during the class. If he didn't like the answer he'd tell them they were lazy or that they should quit college.
dkarl 5y ago
> But the worst part of the experience was the method of starting with epsilon/delta and limits, to "explain" what was going on, and then throwing that away to get on with solving problems using differentials and integrals I guess that was pretty normal once upon a time? I remember that was how my calculus textbooks did it. First pictures to develop some visual intuition, then a gentle foray into how to make the intuitions more rigorous using limits, sequences, and series, and then techniques for solving certain differentiation and integration problems. It makes sense to me; it shows that the techniques are based in math and not in magic, and it lays the groundwork to introduce Taylor series later. It also foreshadows the kinds of proofs that students might do in real analysis if they decide to pursue an engineering or physical science major. I guess every math class could be very different if you knew it was the last math class that students would take, but you don't know that, and it's problematic to separate students according to which ones will study the material further before they're even exposed to it. If a student takes a class and unexpectedly finds they want (or need) to take further classes in the area, they don't want to be find out later that, "Oh, sorry, we didn't think you would pursue this subject, so we gave you the version of the class that didn't prepare you for the next one."