MTH 212 Section 02, Differential Equations, Fall 2008.
11:00AM-12:15PM, Tuesday & Thursday, Liberal Arts Building, Room 218 (Mathematics Computer Laboratory).
Generalities
For Fall 2008 Differential Equations (MTH 212 – section 2) at the University of Massachusetts Dartmouth will be based around a number of specific projects.
The aim of the course is to give you experience in thinking and working about differential equations like an applied mathematician.
Assessment
Assessment will be based on:
- Active group work on specified projects.
- Write-up of solutions.
- Oral defense of your write-ups.
- Final written examination.
Class expectations
1. Participation is expected. This means actively speaking up when you have an idea, when you see how to extend or modify someone else’s thinking, when you think someone else – instructor included – is in error. You are expected, at all times, to express your opinions, feelings and thoughts. Time in class is to be spent working on projects or paying attention when a particular point is being made by the instructor or another student. Being off-task will not be tolerated – this includes web-surfing, reading email, taking cell-phone calls, or generally chatting for extended periods about anything other than differential equations. People who break these class rules will be asked to leave.
2. You must keep regular, dated, records of your work on projects. These MUST be in LaTeX format on a wordpress.com account. To do this you need to have a WordPress account. Please arrange to do this no later than the second class meeting. Email me with your WordPress site and I will add it as a link to this page.
3. Absences, unless due to illness or other unavoidable situations, such as death of a family member, are unacceptable. Failure to attend class regularly – 3 or more unexplained absences – may result in a grade of F, without further discussion. This sounds stringent, but this class is about people meeting regularly to actively participate in mathematical exploration of differential equations Missing classes on a regular basis will not cut it: the community will be weaker without each person’s full and active participation. Please come to class each class session, and participate actively.
Relevant advice from Terry Tao
1. Solving mathematical problems
2. There’s more to mathematics than grades and exams and methods
3. Ask yourself dumb questions – and answer them!
4. Write down what you’ve done
6. Work hard
Resources
The class will be held in the Department of Mathematics computer lab, room 218 in the Liberal Arts Building. The Apple machines in this room are equipped with a variety of mathematical software – Maple, Mathematica and Matlab in particular.
Matlab is available in an Open Source version called Octave, from GNU.
An alternative open source numerical package is SciLab, a scientific software package for numerical computations providing an open computing environment for engineering and scientific applications. Scilab includes hundreds of mathematical functions with the possibility to add interactively programs from various languages (C, C++, Fortran…). It has data structures including lists, polynomials, rational functions, linear systems…), an interpreter and a high level programming language.
A powerful Python based open source mathematics package is SAGE:
Sage can be used to study general and advanced, pure and applied mathematics. This includes a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, exact linear algebra and much more. It combines various software packages and seamlessly integrates their functionality into a common experience. It is well suited for education, studying and research.
The interface is a notebook in a web-browser or the command-line. Using the notebook, Sage connects either locally to your own Sage installation or to a Sage server on the network. Inside the Sage notebook you can create embedded graphics, beautifully typeset mathematical expressions, add and delete input, and share your work across the network.
Check out these videos.
LaTeX
All write-ups of work must be in LaTeX (or a version of TeX). Useful TeX editors are TeXnicCenter and LyX (pronounced “Licks“, unlike TeX which is pronounced “tech”). LyX is probably the easiest to use, particularly in relation to graphics. However, WordPress has a built-in Latex editor. All you have to do to get TeX in WordPress pages is use the command
(remember the “latex” which you do not normally insert when you use a TeX editor). Images are also very use to insert into WordPress pages.
LaTeX manual: The Not So Short Introduction to LaTeX
