# Monthly Archives: April 2014

## MAT3880: Partial Differential Equations through Mathematical Models in Biology

Hi everyone,
If you’re interested in pursuing differential equations further, I highly recommend this course being taught in the fall.
Best,
Prof. Reitz
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Attention Differential Equations Students!
One of the most fascinating and important areas of active mathematical research is Mathematical Biology—the art and science of studying life through mathematics and the mathematics of life.  MAT3880: Partial Differential Equations through Mathematical Models in Biology covers important current topics in this important field.  The course provides a solid foundation in the concepts and methods of partial differential equations within the context of biology
The class meets MW 2:00-3:15pm.

## Office hours today (almost) normal

Hi everyone,

I am in my office from 11am-1pm today, with the exception of a brief meeting from 11:30-12:00.

Best,
Prof. Reitz

## Office Hours, Thursday 4/10/14

Hi everyone,

Today I will be:

1.  In my office from 11:00 – 11:30

2. If no-one shows up, I will be attending an event from 11:30-12:30 – HOWEVER, if you send me an email to: jonasreitz (at) gmail.com, I will get it on my phone and come back to my office to meet with you.

Best,
Prof. Reitz

## OpenLab #3: Flipping the class – Inverse Laplace Transforms and Partial Fraction Decomposition

One of the strongest results from our OpenLab #2 Survey was a request for more examples & problems in class.  As you know, our class time is quite limited – so to take maximum advantage of the time we have, we are going to try an experiment.  This OpenLab assignment, to be completed over the Spring Break, will ask you to get a head start on upcoming material by watching a few videos on the material.  This will hopefully free up some class time for more examples & problems.

Assignment (Due Thursday, April 24, at start of class).  Watch the videos below.  You MUST watch the videos marked “required”.  You CAN also watch the videos marked “optional,” – if you have any questions about today’s lecture, or if you need a reminder of how to do Partial Fractions, you should watch the appropriate videos here.  Test your understanding by completing this problem:

Example. Find the Inverse Laplace Transform of :  $\frac{4 s^2+27}{s (s^2+9)}$

SOLUTION:
Partial fraction decomposition: $\frac{4 s^2+27}{s (s^2+9)} = \frac{s}{s^2+9}+\frac{3}{s}$
Inverse Laplace Transform:  $\cos (3t) + 3$

Then respond to the following prompts.

1. What is one thing you learned from (any) one of the videos? What is one thing that you didn’t understand, or found confusing?
2. Any questions about the example above?
3. Any comment on this assignment? (helpful, confusing, useful, irritating, etc – what did you think of it?)

Extra Credit.  You can earn extra credit by making up a problem and posting it here (do NOT post the solution yourself – let other people solve it!), or by giving a solution to someone else’s posted problem.  Simple problems are fine – it can be much simpler than my example above.  It should be one of the following types of problems:

1. Finding the Laplace Transform (like we did today)
2. Finding the Inverse Laplace Transform, or
3. Partial Fractions

How do I type math formulas on the OpenLab? You can always type mathematical formulas just as you would type them into a TI-83 calculator, for example “sin(2t)+e^x”.  But if you want them to look pretty (like this:  $\sin (2t) + e^x$) you can do that too – here’s a guide (see the section “Typing math on the OpenLab” about halfway down the page).

## VIDEOS – REQUIRED

1. Overview: How do we use the Laplace Transform to solve differential equations?  2 min.  https://www.youtube.com/watch?v=Z_wQvCyKjwE
2. The Inverse Laplace Transform.  6 min.  https://www.youtube.com/watch?v=Y8GXpS31CGI
NOTE: The first minute and a half is a more abstract discussion – follow it as best you can.  BUT hold on for the example, which starts at 1:25.
3. (This is not required, but if you like these videos, he has a whole playlist of videos on the Laplace Transform here:  https://www.youtube.com/playlist?list=PL5750E3CE53DB625A )

## VIDEOS – OPTIONAL

1. Finding the Laplace Transform of a Function:  3 min.  This is a useful example of what we did in class today – it will also help you with WeBWorK 14.
http://youtu.be/ES2Lwzrw_UE
2. Partial Fraction Decomposition – a basic example.  This is a good basic example.
3. Partial Fraction Decomposition – another example. This is a slightly longer example, and it includes a good explanation of how to set up your partial fractions for different kinds of factors in the denominator.

You can find them on the “Grades” page (one of the menu items above).  The Midsemester Grades sheet contains detailed grade information, including your score on Exam #2.  The exams will be returned on Tuesday.

Best,
Prof. Reitz

## Announcements: Exam #2 / Office Hours

1. Exam #2 will be returned on Tuesday (sorry if there was any confusion on this question).
2. Office hours today will be from 11am-12pm.

Best,
Prof. Reitz

## OpenLab #2 Survey RESULTS

Thanks to everyone for completing the survey.  I want to share the results and make some observations.  I’ll follow up with another post discussing possible responses.

### Questions 1-8, rate the usefulness of various activities.

Data. I converted the ratings into a numerical scale from 4 = Extremely Helpful to 0 = Not At All Helpful.  I calculated the average “usefulness rating” for each question – the results are presented below, with the questions listed in order according to their rating.

 QUESTION USEFULNESS RATING 0-4 (Extremely Helpful = 4, Not at all = 0, Don’t Know = not counted) 3. Professor answering questions in class 3.94 5. Email contact with Professor 3.65 1. Lecture 3.60 6. WeBWorK assignments 3.20 4. Office Hours 3.08 2. Group work in class 3.03 8. Working with peers (friends, classmates, other students) outside of class. 2.91 7. Tutoring at CityTech 1.33

Observations. I think it’s telling that the top two items are both about me responding to your questions, either in class or by email – it’s clear that this is important to you (although the one-on-one face-to-face contact provided by office hours is not quite so important, or at least is less convenient).  Group work was generally thought to be useful, but not quite as useful as other activities.  I was surprised to find that outside-of-class resources rated very low, both formal (tutoring) and informal (working with peers).

### QUESTIONS 9 and 10

These questions were short answer, but in each case most of the responses fell into just a few different categories.  I summarized these for each question.

 Q9. What is your biggest challenge in this course? Top Categories Number of Responses Prior knowledge (calculus, algebra, trigonometry) 7 Distinguishing between different types of problems 6 Understanding concepts 4 Remembering steps 3 WeBWorK 3 Organizing your work 2

Observations.  As I suspected, mastery of prior material (both of Calculus and other, earlier topics) is a significant challenge in this class.  Quite a few people talked about the difficulty in determining “which kind of question is which” – books usually focus on one kind of problem at a time, but there is a real need to stop periodically and look at an overview of all the different problem types.  Remembering the steps and keeping your work organized (combined) represent a fairly significant portion, comparable to challenges in conceptual understanding.  I know WeBWorK can be a challenge for everyone, and I’m pleased to see that only three of you listed it as the “biggest challenge”!

 Q10. What could be done to improve your experience of this course? Top Categories Number of Responses More examples 9 More practice 8 More class time 7 Improve WeBWorK 2

Observations.  The responses here were quite clear and fairly uniform – you need to see more examples, you need more practice, and you need more class time!

I’ll think about what changes we might make in response to this data — look for more information in a followup post.

Best,
Prof. Reitz