3 ms·

This reminds me of how much I struggled with integral calc in college. My textbook (Stewart) had a table of integrals containing 120 forms that you'd need to s

This reminds me of how much I struggled with integral calc in college. My textbook (Stewart) had a table of integrals containing 120 forms that you'd need to solve the problems in the book, and looking through them, the calculations seem so insurmountable. Like, https://www.wolframalpha.com/input/?i=integrate+u%5En+sqrt%28a+%2B+bu%29+du https://www.wolframalpha.com/input/?i=integrate+u%5En+sqrt%2... I looked at that and realize that I'd have no future as a physicist and switched to CS.

scrozart 5y ago
IME, Stewart is pretty opaque. The intro section is a great refresher of things you'll need, but the remaining text is pretty muddy. I found an old Thomas Finney book that was much clearer, as was Richard Delaware's YouTube series.
runawaybottle 5y ago
Same textbook. The amount auxiliary material I needed to watch off YouTube to grok it was very real. I had one of those impenetrable profs that only explained calc in the most theoretical terms.
- BearOso 5y ago
  I think the teachers who choose Stewart books don’t necessarily know how to teach down very well, so that would probably be reflected in their lectures, too. In multi-variable calculus I had a Stewart book and the professor put me to sleep. I spent a lot more time figuring it out on my own than I should have. I was too naive to do so, but if anyone out there is in a class and the official suggested book doesn’t help you, ask the Internet for a respected alternative.
  - joshka 5y ago
    I had good teachers and Stewart and did pretty well (2001-ish, not sure how that translates, just one counter point - sorta)
siraben 5y ago
We also used Stewart, and I think struggling (or excelling for that matter) at integral calculus is a poor indicator of one's competency in higher-level math, which is much more than memorizing 120 rewrite rules :)
bntyhntr 5y ago
My AP calc teacher was big into Leithold, specifically TC7 (https://www.amazon.com/Calculus-7-Louis-Leithold/dp/0673469131 https://www.amazon.com/Calculus-7-Louis-Leithold/dp/06734691...) when I had him. Claimed Stewart was useless, but he had a lot of strong opinions. I don't really have anything to say except that I have this feeling that I'm supposed to preach the gospel of TC7 anytime it comes up, so may as well :). Haven't touched calc in 10 years but sometimes still find myself trying to remember the chain rule (usually when miserable on a run)
- klyrs 5y ago
  This paper is an old favorite of mine. It shows how to transform a program that computes the value of a multivariate function into a program that computes that value and all of its first derivatives. The resulting program requires at most 7x more instructions as the original. Spoiler: it's just the rules of differentiation, and the constant 7 comes from the quotient rule. https://courses.cs.washington.edu/courses/cse446/18wi/slides/p60-morgenstern.pdf https://courses.cs.washington.edu/courses/cse446/18wi/slides...
- marcosdumay 5y ago
  > but sometimes still find myself trying to remember the chain rule There's an algebra of differentials that was formalized quite late (I think at the 19th century) but accepts all of the operations you can use for scalars. The chain rule is just fraction simplification.

scrozart 5y ago

IME, Stewart is pretty opaque. The intro section is a great refresher of things you'll need, but the remaining text is pretty muddy. I found an old Thomas Finney book that was much clearer, as was Richard Delaware's YouTube series.

runawaybottle 5y ago

Same textbook. The amount auxiliary material I needed to watch off YouTube to grok it was very real. I had one of those impenetrable profs that only explained calc in the most theoretical terms.

BearOso 5y ago
I think the teachers who choose Stewart books don’t necessarily know how to teach down very well, so that would probably be reflected in their lectures, too. In multi-variable calculus I had a Stewart book and the professor put me to sleep. I spent a lot more time figuring it out on my own than I should have. I was too naive to do so, but if anyone out there is in a class and the official suggested book doesn’t help you, ask the Internet for a respected alternative.
- joshka 5y ago
  I had good teachers and Stewart and did pretty well (2001-ish, not sure how that translates, just one counter point - sorta)

siraben 5y ago

We also used Stewart, and I think struggling (or excelling for that matter) at integral calculus is a poor indicator of one's competency in higher-level math, which is much more than memorizing 120 rewrite rules :)

bntyhntr 5y ago

My AP calc teacher was big into Leithold, specifically TC7 (https://www.amazon.com/Calculus-7-Louis-Leithold/dp/0673469131 https://www.amazon.com/Calculus-7-Louis-Leithold/dp/06734691...) when I had him. Claimed Stewart was useless, but he had a lot of strong opinions. I don't really have anything to say except that I have this feeling that I'm supposed to preach the gospel of TC7 anytime it comes up, so may as well :). Haven't touched calc in 10 years but sometimes still find myself trying to remember the chain rule (usually when miserable on a run)

klyrs 5y ago
This paper is an old favorite of mine. It shows how to transform a program that computes the value of a multivariate function into a program that computes that value and all of its first derivatives. The resulting program requires at most 7x more instructions as the original. Spoiler: it's just the rules of differentiation, and the constant 7 comes from the quotient rule. https://courses.cs.washington.edu/courses/cse446/18wi/slides/p60-morgenstern.pdf https://courses.cs.washington.edu/courses/cse446/18wi/slides...
marcosdumay 5y ago
> but sometimes still find myself trying to remember the chain rule There's an algebra of differentials that was formalized quite late (I think at the 19th century) but accepts all of the operations you can use for scalars. The chain rule is just fraction simplification.