Category Archives: Calculus

A Neat Trick For Determining The Integrals Of exp(x) cos x And exp(x) sin x

The standard method (typically found in first-year calculus textbooks) for determining the integrals and is to integrate by parts twice. If you haven’t seen the standard method, I’ll show you how to do the first one; the second one is … Continue reading

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How Much Mathematics Should A Student Memorize? Part 6, Derivatives Of Exponential And Logarithmic Functions

In teaching calculus many, many times over the years, I strove to present to my students my approach to learning and mastering the subject. Part of this approach can be summarized by the slogan memorize the minimum As a teacher, … Continue reading

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How Much Mathematics Should a Student Memorize? Part 2, Integral Calculus

My basic attitude towards memorization in mathematics education is to memorize the absolute minimum, but memorize that minimum perfectly. Part of a mathematics teacher’s job, in my view, is to guide students to understand what this “minimum” is, and then … Continue reading

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On the fundamental theorem of calculus

One day a graduate student submitted some writing to me, in which she was explaining rates of change at the high school level. She made an interesting statement: The slope of a secant line joining two points (a, f(a)) and … Continue reading

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