Calculus: A Classical Approach

This is the main page for Calculus, Spring 2021. You can find links to all the materials here.

There are three main channels of communication for this class: the course channel on the Bennington Math Slack, the synchronous Zoom classes, and this course webpage.

  • All announcements (including posting of problem sets, scheduling of progress meetings, due dates, corrections, etc.) will be posted on the Slack. I also encourage you to ask questions on the Slack (both of me and of other students), and to have class discussions there.
  • The class time is the main place where the content of the class happens, as well as discussions and collaborative work; please try to attend all classes. Recordings of the Zoom classes will be posted on an unlisted YouTube channel (link in the Slack) in case you miss any.
  • Finally, all problem sets, readings, and other course materials will be linked on this course webpage. Additionally, time permitting, I may write up some lectures or supplementary materials, which I will also link to from here.

Lectures

  • Volumes of Spheres. Shows how to find the volume formula for a sphere. Introduces the general method (“fundamental theorem of calculus”), which will apply not only to volumes but to many different problems.
  • Volume of a pyramid (solution) Gives the solution to the problem posed at the end of the previous lecture, of finding the volume of a pyramid, as well as suggesting some follow-up questions.
  • Differential equations. Talks about setting up differential equation models, interpreting differential equations, and drawing slope fields.
  • Differential equation examples (Problem Set #8). This one mixes a lecture, giving examples of differential equations, together with a problem set. There is some explanation of the problems, examples, and the problems in one document.

Problem Sets

  • Problem Set #1 (assigned Monday February 22, on computing differentials and derivatives; aim to complete by class Thursday February 25)
  • Problem Set #2 (assigned Thursday February 25, on computing differentials for fractions and square roots, and an application to circles)
  • Problem Set #3 (assigned Tuesday March 2, on triangles, Kepler’s first law, area of ellipse, and some applications to circles, spheres, and raindrop growth)
  • Problem Set #4 (assigned Friday March 5, on differential equations, specifically Newton’s law and physics (kinematics) problems)
  • Problem Set #5 (assigned Wednesday March 10, on fractional and negative exponents, their derivatives, and “infinite algebra”)
  • Problem Set #6 (assigned Friday March 19, on computing $\pi$, volume of sphere, chords and arcs of circles (trigonometry), and Pascal’s triangle, the binomial theorem, and infinite algebra)
  • Problem Set #7 (assigned Monday April 12, on volumes and areas, to follow the lecture Volumes of Spheres. Solution to the first problem at Volume of a pyramid (solution).)
  • Differential equation examples (Problem Set #8). This one mixes a lecture, giving examples of differential equations, together with a problem set. There is some explanation of the problems, examples, and the problems in one document. (For that reason I listed it both as a lecture, and as a problem set.)
  • Problem Set #9: Exponentials, logarithms, trig functions. In this final required problem set, I try to elaborate on what we have been doing recently, and to try to tie together some loose ends from throughout the term. (I don’t quite get to it all, for lack of time; if I have time, I will make an “epilogue” problem set that gets at these final loose ends.)

Readings

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