Math Bits - Change of Variables

Prerequisites

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

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 $u$.

Views

New Users

Curriculum

Pedagogy

Institutional Change

Publications