Digital media resources used:
- Powerpoint presentations
In my Math250 class this semester I made lecture notes in Powerpoint format, so that students could use them
to review the material before the exam. I also dedicated a couple of classes to going through the presentations in class,
paying special attention to model problems and outlining the contents of the chapter once again. A lot of them actually printed them out and used them as guidelines when
doing practice exams. Here is one of the presentations I created:
Chapter 1 slides (Powerpoint converted to PDF, 152KB)
- Digital video clips
This is a Quicktime clip showing construction of a Fourier series. This movie is a free web-based resource and was meant to
complement the lecture material in my Spring 2002 Math251 class. I asked students to look at this movie and several other
applets at home to broaden their understanding of the subject.
Fourier series movie (2.35MB, needs
Quicktime to play)
(Description: The clip runs for about 5 seconds. It shows harmonic functions with higher frequencies being suporposed with lower frequency ones. The more functions enter the picture, the better it approximates the curvy shape of the Fourier series. Limiting behaviour is shown at the end.)
- Graphics and pictures for overhead transparencies
When you're running a course that is very intense and packed tight with all kinds of material, there are situations when
you have to pick - either you make students see the "big picture" before doing examples and explaining technicalities, or
you jump into examples right away, leaving abstract concepts aside. I personally prefer having a theoretical
background of some kind before proceeding to explore examples and special cases, but I came to realize that most of the
students in engineering sequence do not follow this material well unless provided with proper motivation. That is why I
usually make a compromise: I bring a couple of transparencies to class and walk through some theory and
several model examples before discussing concrete and down-to-earth examples. This way it doesn't take so much
time, so I manage to keep their attention, and they do get a bigger picture left in their heads before crunching in the
numbers. Sometimes I also use overhead to show graphs which are difficult to reproduce or look better in colors than drawn on
the board. Here are some of the pictures I used with the overhead transparencies:
Model word problem: mixture (PDF, 104KB)
Graph showing implicit vs. explicit solution (PDF, 556KB)
The pictures in these slides were produced with MATLAB as EPS first, then were incorporated into a LaTeX file and converted
to PDF.
- Homework/quiz solutions with LaTeX and PDF
For several semesters now I've been providing my students with online solutions to all homeworks, quizzes and group
projects assigned in the course. I've also scanned all practice exams I found and made solutions to them available on the
web. I know my solutions have been widely popular in student community, and not only to students in my sections, and I
think it did help them a lot in understanding of basic math concepts, since they tried to mimic the arguments in their
own solutions. The format I found works best for the online documents, especially when it comes to the questions of
platform independence, is a LaTeX-compiled PDF format. In fact, I try to make PDF files out of all other formats as well
to avoid possible complications. Here are some examples:
Homework 3 solution set (PDF, 60KB)
Project 1 solution set (PDF, 41KB)
Calculus formulae sheet (PDF, 111KB)
The last one of these is a list of formulae I made for my students in the beginning of the semester. Since the knowledge of
these formulae is essential to mastering the material of any differential equation course, I made my students review and
memorize this list and tested them with a small preliminary quiz the first week of classes. Not only it made them go back
to long forgotten calculus material, but it also made it possible to me to identify the students who came with a weak background
and needed some additional help.
- Interactive applets and MATLAB software
One undoubtable advantage of modern teaching is an availability of extensive web-based resources which a teacher can
incorporate into the stream of a course. I'm very grateful to Prof. Chartier, Prof. White and many other extraordinary
teachers whose courtesy allowed me to brighten the contents of my courses with colorful and concise pictures and Java
applets. The first and the third applets listed below were demonstrated in class to give an insight into the topic of the
lecture.
Falling Body tool
Direction fields applet
Fourier series applet
The second link above is an applet students used to construct direction fields in my Math250 and Math251 courses.
There were a couple of alternative software tools they were allowed to use, such as MATLAB "dfield6" script or Moses
Glasner's Java applets. I used MATLAB a lot while teaching these courses to demonstrate the use of direction fields in class
and to produce the solution sets for homework assignments. You're being invited to look at the Homework 1
solution set for Math250, for instance, which contained several direction field pictures.
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