Tag Archives: calculus

Sequences and series

Me: “Calculus is basically just a sequence of lies.” JY: “Or a series of lies. [pause] Which is really just a sequence of partial lies.”

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1 + 2 + 3 + 4 + …

There’s a video that has gone viral and concerns itself with the equation . A couple of students from my Calculus 2 class last semester sent me the following e-mail, which makes me smile for several reasons: We are rather … Continue reading

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Short exam

I gave a short (half-hour instead of 50-minute) exam as the last in-class exam in my calculus 2 class this semester. (We also have a big final exam at the end of the term.) Student feedback afterwards was surprisingly positive … Continue reading

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Calculus wrap-up

Twice as many students showed converges by showing that for n sufficiently large (and so the series converges absolutely by comparison with a p-series for ) than by observing that the series in question is a geometric series. Many of my students … Continue reading

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Exam statistics

After removing two outliers, the correlation between scores on exam 1 and 2 in the class I’m teaching was 0.24.  This seems surprisingly low to me; has anyone with more experience seen similar numbers before?  The correlation between p-set scores … Continue reading

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Footnotes: Taylor and Bernoulli

G. F. Simmons, Calculus with Analytic Geometry, footnote, p.495: Brook Taylor (1685-1731) was secretary of the Royal Society and an enthusiastic supporter of Newton in his acrimonious controversy with Leibniz and the Bernoullis about the invention of calculus. Taylor published … Continue reading

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Generating series

Last Wednesday morning lecture, to calculus students, in two sentences: A series that looks like is called a Taylor series.  We are very interested in understanding these series and the functions they represent, so it is of the utmost importance … Continue reading

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