QuickBASIC and Visual Basic programs
(Dr. Glyn George)

More recent Minitab sessions, Excel files and macro programs can be found in the web site for ENGI 4421 Probability and Statistics.   Available elsewhere are some demonstration files for Stella and Excel, including   array names and matrix functions in Excel.

Available here is an Excel speadsheet to find the determinants, inverses and products of pairs of 2×2, 3×3 and 4×4 matrices and to find the eigenvalues and eigenvectors of 2×2 matrices.   The derivation of the eigenvalues and eigenvectors is in an associated PDF file.

Below is a list of some of the QuickBASIC programs that I developed several years ago for various mathematics courses that I taught in the Faculty of Engineering and Applied Science.

Anyone reading these pages is free to copy and use the QuickBASIC source code files listed below, provided that due credit remains attributed to Dr. Glyn George of the Faculty of Engineering and Applied Science, Memorial University of Newfoundland.

Linear Algebra:

linsys.exe:	Click on this link to run the Visual Basic program, which does the arithmetic of row operations in the reduction of a linear system.   However, the user has to choose which row operations to perform. All coefficients are handled as rational numbers.
Source code	for the Visual Basic program

Also available is the original QuickBasic version of this row reduction program:

linsys.bas

Geometry:

line-eqn.bas:	find the equation of the line joining two points. All numbers are handled as rational numbers (fractions).
epicyc.bas:	build up epicycloids of n cusps from chords of a guide circle. Click here for a stand-alone executable version of this program.
limacons.bas:	sketch a limaçon (polar equation r   =   k + cos q ).
polars.bas:	sketch the polar curves r   =   cos(n q )   for n = 1, 2, ..., 6 .
trochoid.bas:	sketch a trochoid curve (the cycloid is a special case).

Three versions of a program to sketch conic sections as the eccentricity changes:

conics1.bas:	fixed centre and vertices (foci and directrices move)
conics2.bas:	one fixed focus and vertex (centre, directrices and other focus, vertex move)
conics3.bas:	fixed directrices and centre (foci and vertices move)

Also:

Background information is in the article “Visual Appearance of Superluminal Circles ”, for the following three programs, all of which simulate the visual appearance of a circle moving faster than light:

circle.bas:	observer in the plane of the circle
circle2.bas:	observer above the plane of the circle, directly over the path of the centre.
circle3.bas:	observer above the plane of the circle; fish-eye-lens view of the plane.
circle3.exe:	Directly executable version of the above file.

Calculus:

bin-expn.bas:	find the first few terms of a binomial expansion   (1 + x )n.
taylor.bas:	plot Taylor polynomial approximations to   y   = cos x .

There is also a set of Excel spreadsheet files to illustrate Taylor polynomials and remainder terms, in the ENGI 1405 web site.

Probability and Statistics:

As noted above, most demonstration files for this subject are described on a separate web page, at this link.   Some older QuickBasic programs are listed here:

birthday.bas:	A simulation of the classic result that in any group of 25 randomly chosen people, it is odds-on that at least two will share a common birthday.
clt.bas:	A demonstration of the Central Limit Theorem.
cointoss.bas:	Evolution of the relative frequency of heads with ever more tosses of a fair coin.
hyp-test.bas:	An illustration of type I errors in hypothesis testing.

There is also a set of Excel spreadsheet files and Minitab session files to illustrate various concepts, in the web site for this course.

Not from any class   (mostly Number Theory):

baseconv.bas:	conversion from base 10 decimals into numbers of any other base from 2 to 62.
attract.bas:	interesting patterns from plotting the successive values of the partial sums   xn = 3 cos(id ), yn = 3 sin(id ).
queens.bas:	finds all solutions to the N queens problem on an   N × N chess board.
salamin.bas:	a very efficient algorithm for calculating p.

Also included here are two versions of a stand-alone executable file created with Microsoft Visual C++ to demonstrate complex number arithmetic:

• complex.exe
• complexOld.exe   -   If you execute this older program, then please note the following quirks:
  • a negative sign cannot be entered first, but must be inserted in front of an existing digit, and
  • a decimal point can be entered only between two existing digits.

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