Appendix A
CSODE User's Guide
Computer Solutions of Ordinary Differential Equations (CSODE) is a col-
lection of six computer programs written in Microsoft Visual Basic 6 designed
to execute in the Microsoft Windows environment. The software CSODE is
on the computer disc which accompanies this text. Copy CSODE onto your
desktop. Then to run CSODE double click on the CSODE icon.
The name and purpose of each computer program on CSODE is as follows.1. GRAPH- Graphs any function y = f(x) in the rectangle
R = {(x,y) I Xmin :<::: x :<::: Xmax and Ymin:::; y:::; Ymax}.
2. DIRFIELD- Graphs the direction field y' = f(x, y) in a rectangle R.
3. SOLVEIVP- Solves the initial value problem y' = f(x, y); y(c) = d on
t he interval [a , b] where c E [a , b].- POLYRTS- Finds all roots of a polynomial with complex coefficients of
degree less t han or equal to ten. - EIGEN- Calculates the eigenvalues and eigenvectors of a real n x n
matrix A where 2 :<::: n :<::: 6. - SOLVESYS- Solves a vector initial value problem consisting of a sys-
tem of n first-order differential equations and n initial conditions on an
interval [ a, b] where 2 :<::: n :<::: 6.
BASIC is an acronym which stands for Beginner's All-purpose Symbolic
Instruction Code. The language BASIC was initially developed in the 1960 s by
Dartmouth Professors John Kemeny and Thomas Kurtz. In order to run the
programs POLYRTS and EIGEN, all you need to know is how to enter integers
and real numbers into the program and how to read output which contains
an exponential notation similar to scientific notation. In BASIC, an integer
constant is an integer between -32768 and 32767 written with no commas
and no decimal point. Real constants appear in two varieties- fixed-point
constants and floating-point constants. Both contain a decimal point (usually)
and no commas. For example, 3.14159 is a fixed-point constant, six digit
approximation for 1r. A floating-point constant consists of an integer constant
or fixed-point constant followed by the letter E (for single precision) or D (for
double precision) and a signed integer (the exponent). For example, 234E5
499