# Math Bits - Change of Variables

## Prerequisites

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

## In-class Content

• Reading/Lecture: QMSHO (Lecture: 25 min)

## 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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