Link to this document's Jupyter Notebook

In order to successfully complete this assignment you need to participate both individually and in groups during class. If you attend class in-person then have one of the instructors check your notebook and sign you out before leaving class. If you are attending asyncronously, turn in your assignment using D2L no later than 11:59pm on the day of class. See links at the end of this document for access to the class timeline for your section.

Welcome to CMSE / MTH 314

What can you solve with $Ax=b$?

Visual image of three planes intersecting. This is a common image used in linear algebra and will be explained in detail laater in the semester. It is included here mostly as a visual anchor that can help students when they review their notes.

Image from http://wikipedia.org/

from IPython.display import YouTubeVideo
YouTubeVideo("-aiL8iWhQjc",width=640,height=360, cc_load_policy=True)

Agenda for today's class (80 minutes)

  1. (10 minutes) Class Procedures
  2. (10 minutes) Pre-class Survey
  3. (10 minutes) Example
  4. (25 minutes) Syllabus, Schedule and other Procedures
  5. (5 minutes) Download and review next pre-class assignment

1. Class Procedures

All in-class assignments are designed such that you can get started as soon as you show up in class. This is highly recommended. See how far you can get on your own and then you will be ready when it is time for questions. Here are the basic instructions.

✅ Step 1 - Get out your laptop

Feel free to grab one of the laptops in the classroom if you do not have your own.

✅ Step 2 - Activate your engineering account

When you enrolled in class you should have received an engineering login. Go to the following URL to activate the account and set your password.

NOTE: The Default DECS password is APID then the @ symbole.

ALSO NOTE: Anyone not enrolled in the course will likely not have an account.

✅ Step 3 - Download this jupyter notebook

Go to the Course website, click on "Download Assignments" and download a copy of this notebook by clicking on the (ipynb) link (ipynb stands for ipython notebook).

✅ Step 4 - Log onto the Engineering JupyterHub Website

http://jupyterhub.egr.msu.edu

✅ Step 5 - Create a CMSE314 Assignment Folder in your home directory

HINT Store all notebooks in the same folder on your computer. They will work better that way.

✅ Step 6 - Upload this notebook to newly created folder on Jupyterhub

Once the notebook is uploaded, open it and do the pre-class survey

✅ Step 7 - Sign in to the course slack channel.

We will be using a slack channel for all asynchronous in-class discussions. My hope is to use this as the primary way to communicate with students outside of class. Therefore I hope everyone will get a slack account. If for some reason you decline to get a slack account, please let me know and I will find a way to accommodate an alternative.

To join the course slack channel please use the following link:

2. Pre-class survey

Run the following cell to embed the pre-class survey into this notebook:

Direct Link to the pre-class survey

from IPython.display import HTML
HTML(
"""
<iframe 
	src="https://forms.office.com/Pages/ResponsePage.aspx?id=MHEXIi9k2UGSEXQjetVofVsFhDFfo_lLkU7qIzY8I4ZUMlJQN1BJSzJIQlFRVE5INlNKUjVQTDBFQy4u" 
	width="100%" 
	height="1000px" 
	frameborder="0" 
	marginheight="0" 
	marginwidth="0">
	Loading...
</iframe>
"""
)

3. Example:

Suppose that we have three objects on a balanced beam. Also suppose we know that one has a mass of 2 kg, and we want to find the two unknown masses. Experimentation with a (assume weightless) meter stick produces these two balances. (diagram not to scale)

Image showing two balanced beams, each with three weights. In the top beam is unknown weight A is a distance of 40 to the left of the fulcrum, unknown weight B is a distance of 15 to the left of the fulcrum and a weight of 2 is 50 to the right of the fulcrum. In the bottom beam is the same unknown weights. Weight A is now a distance of 50 to the right of the fulcrum, weight B is a distance of 25 to the left of the fulcrum and the weight of 2 is a distance of 25 to the right of the fulcrum.

For the masses to balance we must have the sum of the moments on the left equal to the sum of the moments on the right, where the moment of an object is its mass times its distance from the balance point. That gives a system of two equations:

$$ 40A + 15B = 50 \times 2$$$$25B = 25 \times 2 + 50A$$

✅ Do This: Find a solution for the above systems of equations and place your solution in the following cell. Make sure you delete the instructional text in the cell first.

# Put your answer to the above question here

✅ Do This: Using Python as a calculator, verify that the solution you have found is correct.

# Put your answer to the above question here

✅ Do This: Now lets consider a system where we have three unknown masses instead of two. Experimentation with a meter stick produces the two balanced states shown below (diagram not to scale). Write the equations for this system.

Image showing two balanced beams, each with four weights. In the top beam is unknown weight A which is a distance of 35 to the left of the fulcrum, unknown weight B is a distance of 21 to the left of the fulcrum, unknown weight C is a distance of 11 to the right of the fulcrum and a weight of 2 is 50 to the right of the fulcrum. In the bottom beam is the same unknown weights. Weight A is now a distance of 10 to the right of the fulcrum, weight B is a distance of 24 to the right of the fulcrum, weight C is a distance of 25 to the left of the fulcrum and the weight of 2 is still at a distance of 50 to the right of the fulcrum.

Put your answer to the above question here

✅ Do This: Find a solution to the second set of equations and report the mass for objects A, B and C.

# Put your answer to the above question here

✅ Do This: Using Python as a calculator, verify that the solution you have found is correct.

# Put your answer to the above question here

4. Syllabus, Schedule and other Procedures

Note: I will try to include these links at the end of every pre/post class assignment so you can easily navigate.

Upcomming Assignment Due Date:

Pay attention to the schedule. Every class has a pre-class assignment that should be completed. There is also a major assignment due every week (either a quiz or a homework).

  • Your First Quiz is the scheduled on the second session (04) the week of Monday September 14th. and will cover topics up to that Date (including the 04-pre class assignment).
  • Your First Homework is due Friday September 25th.

5. Download and review next pre-class assignment

I will try my best to post each weeks pre-class assignments before the weekend (hopefully on Thursday before class). Note pre-class assignments are generally due at midnight the day before class. To get credit for the pre-class assignment you will need to do the readings, answer the questions and submit your answers to the embeded google form.

Here is next week's Pre-class assignments.

Please note Please see the course schedule (link on the course website) for a list of assignments and the due dates for your section.

Congratulations, we're done!

If you attend class in-person then have one of the instructors check your notebook and sign you out before leaving class. If you are attending remote, turn in your assignment using D2L.

Course Resources:

Writen by Dirk Colbry, Michigan State University Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.