Math Bits - Change of Variables


Students should be able to find derivatives of unspecified functions, especially using the product rule.

In-class Content

Additional Content

Student performance

Here are some notes regarding students' performance on the quiz in 2018, which covered change of variables (from Karan, who graded the quiz):

  1. Since, Weihong mentioned in class that second derivative is not the Square of the first derivative, there were only 2 students who did that.
  2. There were still a majority ( 8-9) students who zapped the equation TWICE to get d^2 operator.
  3. Then there were some students ( 4-5) who tried using chain rule and messed up on the second derivative.
  4. Students who were correctly able to change the first and second derivatives ran out of time/ made algebra mistakes. For those students, I didn't take any points off.

Homework for Central Forces

  1. (ChangeDerivative)

    Consider the differential equation $z^2y^{\prime\prime} + zy^{\prime} - (1-z)y = 0$. (This is known as Bessel's Equation.)

    1. Using the change of variable $u = 2\sqrt{z}$, rewrite Bessel's Equation in terms of $u$.

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