Month: October 2023 (Page 2 of 3)

Class Info

• Date: Mon Oct 23
• Meeting Info: 12p-1:40p, N700

Announcements

WebWork: “Derivatives – Rates of Change” — extended to next Monday (Oct 30)

Topics

We through some examples from “Derivatives – Rates of Change”. In all of these exercises, we are given a “position function” which gives the positition of the moving object as a function of time. We take the derivative of the position function to get the velocity function v(t):

Here is a video with a similar example:

Class Info

• Date: Mon Oct 16
• Meeting Info: 12p-1:40p, N700

Announcements

We will have our first midterm exam (Exam #1) on Wednesday. See below for a list of topics and exercises to to review.

Topics

We spent the class reviewing for the exam. The main topics we have covered so far this semester and which which will be covered on the exam are:

• the limit definition of the derivative
• finding the equation of a tangent line at a given point (using the derivative to find the slope), and sketching such a tangent line for a given graph/point
• the differentiation rules

These topics were covered in the two quizzes, so you can start by reviewing the quiz solutions, which are available via OpenLab Files.

You should also understand this graph, which is related to the limit definition of the derivative (how the difference quotient arises as the slope of a secant line):

For the limit definition of the derivative, we reviewed Exercise #1 from the WebWork “Derivatives – Limit Definition” and also Quiz #1. (You can see further details on the WebWork exercise in the Class 4 Recap.)

For the differentiation rules, you can review the “Power Rule”, “Product Rule” and “Quotient Rule” WebWork sets. You can also review the differentiation examples we did in Class 7, Class 8, Class 9 and Class 10.

We also went through Quiz #2 in detail, which covered the Power Rule and the Product Rule, and writing the equation of a tangent line:

We also went through a Quotient Rule example, based on the functions from Quiz #2:

Class Info

• Date: Tues Oct 10
• Meeting Info: 12p-1:40p, N700

Announcements

We will have a quiz tomorrow (Wed Oct 11), covering the various differentiation rules (power rule, product rule, quotient rule). You don’t need to memorize the rules–they will be provided on the quiz.

Topics

Why are we interested in derivatives? Slopes of tangent lines (which provides a lot of “geometric” information, i.e, about the shape of the graph of the function:

Derivatives as rates of change

We went through this WebWork Quotient Rule exercise, where P appears to be some physical quantity (Pressure?) expressed in terms of V, R and r (perhaps a volume and two separate radii?):

The exercise tells us to treat R and V as constants, and to calculate dP/dr, i.e., the rate of change of P(r) with respect to the independent variable r, for which we use the Quotient Rule:

We then started discussing Sec 3.4, “Derivatives as Rates of Change” — specifically in the context of “motion along a line”:

Example 3.34 from the textbook: