The semester is officially 15 weeks in length but in practice, due to holidays, is more like 14 weeks.
The course will be structured around four 3-week blocks, with a mid-semester poster presentation after the second and fourth 3-week block.
First 3-week block
In the first class of the semester we will deal with a number of administrative matters. First, you will get to know me and I will get to know you. I will have a class list, that may require some modifications due to drop-outs and add-ins. I will work hard at getting to learn your names as quickly as possible. My memory is nowhere near as good as it once was so this might take longer than I would wish for. Please bear with me and be kind if I forget your name or make a mistake.
In the first class we will deal with class expectations. I will take time to walk you through what is on the home page of this site so that you understand my expectations for behavior in class, and for attendance.
At this time I will also go through the structure of the course, as is written here, and through assessment, as is detailed below.
During the first class I will introduce you to a simple differential equation, and some techniques for analyzing the behavior of solutions to this differential equation.
This example, which I will most likely continue to expand on in the second class session, will serve as a model for the work I want you to carry our for the remainder of the first 3-week block.
The exemplar differential equation to be analyzed in class can be found here.
Second 3-week block
The theme for this block is numerical approximation of solutions of differential equations. In the first class of the block I will go through an example of a non-linear system of differential equations for which there is no known analytical formula for a solution. We will examine such solutions numerically, using Euler’s method and Runge-Kutta methods.
Third 3-week block
The topic for this block is linear systems of differential equations. In the frist lecture of the block I will go through examples of systems of two linked linear differential equations.
Fourth 3-week block
In this block we will tackle both series solutions of differential eqations and Lapalce transforms.
Assessment
First the good news: there are no written tests, no written quizzes, no written mid-semester examination, and no homework assignments.
Now for the reality!
1. I will keep a card for each student in the class. I will regularly ask students to explain their work to me in class. Sometimes this will be an explanation one-on-one with me personally, other times it will be a brief presentation to the whole class. At such times I will grade the response from you as one of : VERY GOOD (2 points), OK (1 point) or NO GOOD (0 points). I will ensure that each and every student is asked on a fair and equitable basis, and will discuss earned points with you at the and of each 3 week block. What this mean in practice is that you need to be both paying attention and working on-task each and every class. That’s the trade-off for no homeworks.
2. In each 3 week block you will work in a group assigned by me. With the working guidelines for the blocks as described above, you and your group will work on a task of your choice from a list of possibilities for that block. You and your group will write your work, collectively in a wordpress.com page using LaTeX, and you, personally, will be prepared to defend and explain what your group has written.
I will conduct a brief oral examination of each student at the conclusion of the second and fourth 3-week blocks to ascertain whether you have an understanding of what your group has written.
There will also be a final examination in which you will write an account of the work you have carried out in each of the four 3-week blocks.
Extra credit
You can always earn extra credit for doing two things:
1. Giving clear written explanations of aspects of the texts or aspects of differential equations that are puzzling you or other people.
2. Giving clear class presentations of aspects of the texts or aspects of differential equations that are puzzling you or other people.
