MAT1475 – Calculus 1

Instructor: Suman Ganguli | Fall 2023

Month: November 2023 (Page 2 of 3)

Class 20 Recap (Wed Nov 8)

November 9, 2023 / / 0 Comments

Class Info

  • Date: Wed Nov 8
  • Meeting Info: 12p-1:40p, N700

Announcements

WebWork:

  • “Derivatives – Chain Rule” – due Friday Nov 10
  • “Derivatives – Exponential” – due Friday Nov 17

Topics

We reviewed the derivatives of the exponential function and the natural logarithm function (covered in Sec 3.9 of the textbook):

We did some examples involving derivatives (and “higher” derivatives) involving exponential functions (and applying the Chain Rule):

Here is another 3blue1brown video to watch, about the exponential function(s) and the number e (in the context of calculus):

Class 19 Recap (Mon Nov 6)

November 7, 2023 / / 0 Comments

Class Info

  • Date: Mon Nov 6
  • Meeting Info: 12p-1:40p, N700

Announcements

WebWork:

  • “Derivatives – Chain Rule” – due Friday Nov 10

Quiz:

  • We will have a quiz tomorrow (Wednesday). The quiz will have a rate of change (position/velocity) exercise, and some derivatives involving trig functions and the Chain Rule.

Topics

We first went through a Chain Rule exercise from the WebWork which involved writing the equation of a tangent line. We used this to again discuss the idea of a tangent line as a “linear approximation” for a nonlinear function:

We then reviewed the exponential function y = e^x, and introduced its derivative: it is its own derivative!

We illustrated this with by writing the equation of the tangent line for y = e^x at x = 3, and calculating derivatives of various functions involving exponential functions:

We also reviewed the logarithmic functions, which are the inverses of the exponential function–in particular the “natural log” function ln x, which is the inverse of e^x. We will work with the derivative of ln x next time.

This material is covered in Sec 3.9 of the textbook.

Class 18 Recap (Wed Nov 1)

November 2, 2023 / / 0 Comments

Class Info

  • Date: Wed Nov 1
  • Meeting Info: 12p-1:40p, N700

Announcements

WebWork:

  • “Derivatives – Trigonometric” — extended to Monday Nov 6
  • “Derivatives – Chain Rule” – due Friday Nov 10

“Plan” Week:

  • This is Plan Week at CityTech: “Plan Week activities are designed to prepare you for advisement and registration for summer and/or fall and beyond, and to ensure you are taking the right courses and asking the right questions to stay on the path to graduation and achieving your future goals.”
  • See the Plan Week website here.

Topics

We went through the Chain Rule again and worked through a number of examples, including some from the “Derivatives – Chain Rule” WebWork set.

We also viewed parts of this PatrickJMT video, which I posted in the previous Class Recap, and discussed some of the examples in the video:

https://www.youtube.com/watch?v=6kScLENCXLg

See also the examples in Sec 3.6 of the textbook.

We closed with an example of a “nested Chain Rule”:

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