3020 Differential Equations, Fall 2013
Textbook:
P. Blanchard, R.L. Devaney and G.R. Hall, Differential Equations,
3rd or 4th edition, Brooks/Cole Publishing Co.
In addition to that, there are about 20 books available in the NCCU library
with the words "Differential Equations" in the title. You may consult me
whether any given book is appropriate for this course or not.
A very brief synopsis of topics covered so far
(pdf file)
Software:
Octave.
Octave is mostly Matlab compatible, so one may use the same code for
Octave and Matlab. Try to follow the installation instructions at their
download page.
In a nutshell, if you are using Linux or MacOSX, you should be fine,
if you are using Windows, you should install
Cygwin with the full X Window support,
then install Cygwin packages "octave" and "gnuplot", and then
you will be fine too.
A sample of Octave code (used in the class) to draw the slope field of the
differential equation \(y^\prime = y - x\):
f = @(x,y)y.-x;
[x,y] = meshgrid (-2:0.1:2);
slopes = f(x,y);
dx = 0.1 ./ sqrt(1 + slopes.^2);
dy = slopes .* dx;
quiver (x,y,dx,dy,0);
LaTeX.
You may (and, in fact, are highly enocouraged) to type your homeworks and
projects using LaTeX.
You may ask me for help with installation, usage, or any other
software-related issues.
Homework 1 (pdf file),
due September 3, 2013.
Homework 2 (pdf file),
due September 17September 19, 2013.
Project 1, due August 29, 2013
Read Appendix B of the texbook.
Solve the differential equation \( \frac{dP}{dt} = kP \) by the power series
methods.
You can get for it up to 2 extra points.
Project 2, due September 12, 2013.
Read Section 1.1 of the texbook.
Try to invent a situation which can be modelled by a differential equation or by
a system of differential
equations. This can be either a situation from the real life, e.g. from your work
or hobbies, or a purely fictious one - from science fiction movie,
your favorite cartoon, etc. (e.g., instead of foxes and rabits from the textbook
you may think of one alien race chasing another, etc.)
The obtained differential equation(s) should be nontrivial enough
(e.g., \(\frac{dP}{dt} = 0\) does not qualify), and different from all the
examples we have considered in the class.
Make a qualitative analysis of it.
What are equlibrium solutions? When the solutions increase? Decrease?
Can you write an approximate graph of solutions?
Try to solve your differential equation(s) by all the methods we learned so far.
You can get for it up to 5 extra points.
Project 3, due September 17September 24, 2013.
Modify the Octave code above:
-
to make the small arrows representing the slopes
not to start at the points in the grid, but be centered around them;
-
to draw the coordinate axes x and y.
If you wish so, use not Octave, but any other software package and/or environment
to achieve the same goal.
You should be able to demonstrate to me and/or in the class how the code works.
You can get for it up to 3 extra points.
Project 4, due September 19September 24, 2013.
Read section 1.4 of the textbook.
Write a computer code, in Octave or any other programming language/environment,
implementing Euler's method. Take an initial value problem for which
the solution can be found by an analytic method (say, a separable one), plot
the graph of the solution, and plot the points computed by the Euler's method.
You can get for it up to 4 extra points.
Created: Fri Aug 23 2013
Last modified: Thu Oct 19 18:38:58 CEST 2017