Class 26 Agenda

Class Info

  • Date: Thursday, December 2, 2021, 2:30-3:45pm
  • Meeting InfoClass will meet asynchronously today – this means you do NOT have join our usual zoom link, but you DO need to review todays online lesson and work on the associated WeBWorK assignment (see “Activities” and “TO DO after class” below).
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Lesson 26: Inverse Laplace Transform

Hi everyone! Read through the material below and watch the videos, then give the WeBWorK assignment a try.

Lesson 26: Inverse Laplace Transform

Learning Outcomes: At the end of this lesson you will be able to find the inverse Laplace transform of functions

Topic. This lesson covers section 8.2: The Inverse Laplace Transform.

WeBWorK. There is one WeBWorK assignment on today’s material: Inverse Laplace Transforms

Review: Finding the Laplace Transform of a function

You may wish to refer to this Table of Laplace Transforms during today’s lesson.

Example 1.  Find the Laplace Transform of each function, and determine the interval on which it is defined.

  1. t^{2}+4 t^{3}-7 t^{6}
  2. \sin t+\cos 3 t
  3. 5 e^{2 t}-4 \sin 3 t
  4. 5 t^{2}+3 \sin 5 t-2 e^{6 t} \cos 2 t

Find the inverse Laplace Transform

Now we consider the inverse problem – if I give you the Laplace Transform of a function, can you find the function it came from?

Example 2. Find the inverse Laplace Transform of each function.

  1. \frac{3}{s}+\frac{4 !}{s^{5}}+\frac{1}{s-7}, \quad s>7
  2. \frac{1}{s^{2}+25}+\frac{s}{s^{2}+25}, \quad s>0
  3. \frac{1}{(s-4)^{2}+9}, \quad \mathrm{~s}>2
  4. \frac{1}{(s-6)^{7}}+\frac{5}{2 s-7}, s>6
  5. \frac{5}{s^{2}-8 s+41}, s>4

That’s it for today! Try out the WeBWorK assignment, and let your professor know if you have questions.

Exam #3 and Project grades are posted on OpenLab

Hi everyone,

Grades for Exam #3 and the Numerical Methods Project are available through the OpenLab Gradebook.

For the exam, a link to your graded exam paper is in the Gradebook comments.

Please note that your exam grade will not be finalized/available until you have completed your one-on-one meeting with me – if you still need to do this, please send me an email and we will find a time.

Best,
Prof. Reitz

Request to push back exam – any objections?

Hi everyone,

I’ve received several requests to delay the exam until after the Thanksgiving break (Tuesday 11/30). I am willing to consider this, although I do not like making changes on the day of the exam itself. I’m posting this in case anyone has an objection to moving the exam to Tuesday, 11/30/21 instead of today – if you do, please email me at jreitz@citytech.cuny.edu this morning!

Best,

Prof. Reitz

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