Normal distributions and exp(-x^2) are sort of the exceptional case. Any reasonable study of probability and statistics will include probability density functions, which you can’t talk about at all unless you explain integrals.
Of course, exp(-x^2) is harder to integrate than most pdfs (naturally occurring or artificial) that you’d run into. I wouldn’t expect someone who learned enough calculus to understand integrals to know enough to integrate it. But before teaching someone to look values up in a table, I would want them to understand that the probabilities they’re finding are an integral of the pdf, for intuition purposes.
I agree that the year-long calculus sequence that is the norm at most colleges is probably overkill for non-mathematicians, even ones that need to know some calculus. But the basic facts of calculus enhance understanding of a whole bunch of related ideas.
I wonder if it would work well to teach a calculus class which only focused on concepts and excluded any calculation whatsoever of derivatives and integrals—given that Internet access is sufficient to integrate or differentiate any function you come across, those skills seem less relevant now.
Normal distributions and exp(-x^2) are sort of the exceptional case. Any reasonable study of probability and statistics will include probability density functions, which you can’t talk about at all unless you explain integrals.
Of course, exp(-x^2) is harder to integrate than most pdfs (naturally occurring or artificial) that you’d run into. I wouldn’t expect someone who learned enough calculus to understand integrals to know enough to integrate it. But before teaching someone to look values up in a table, I would want them to understand that the probabilities they’re finding are an integral of the pdf, for intuition purposes.
I agree that the year-long calculus sequence that is the norm at most colleges is probably overkill for non-mathematicians, even ones that need to know some calculus. But the basic facts of calculus enhance understanding of a whole bunch of related ideas.
I wonder if it would work well to teach a calculus class which only focused on concepts and excluded any calculation whatsoever of derivatives and integrals—given that Internet access is sufficient to integrate or differentiate any function you come across, those skills seem less relevant now.