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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.”
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 email, which makes me smile for several reasons: We are rather … Continue reading
Posted in Education, Math
Tagged analytic continuation, calculus, convergence and divergence, Taylor series
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Short exam
I gave a short (halfhour instead of 50minute) exam as the last inclass 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
Calculus wrapup
Twice as many students showed converges by showing that for n sufficiently large (and so the series converges absolutely by comparison with a pseries for ) than by observing that the series in question is a geometric series. Many of my students … Continue reading
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 pset scores … Continue reading
Footnotes: Taylor and Bernoulli
G. F. Simmons, Calculus with Analytic Geometry, footnote, p.495: Brook Taylor (16851731) 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
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