Don't forget to press ESCAPE to remove a help screen.
This is where you can view all the differential equations, solutions, and power series that you have created.W
Use this to create 2nd order ordinary differential equations of the type
y" + p(x)y' + q(x)y = f(x),
subject to the initial conditions
y = y(x0), y' = y'(x0).
The functions p(x), q(x), and f(x), may include parameters a, b, and c. Up to 10 ODEs can be created.
If you press the INSERT key while creating p(x), q(x), and f(x), a list of functions is displayed. You can use and edit these, or create your own functions from scratch. You will also be expected to supply the point x0, and the initial values y(x0), and y'(x0).
There are a few points to remember.
Exponentiation is represented by the "^" key, so that 10^2 = 100.
Also x^3/2 = (x^3)/2, NOT x^(3/2), and 1/x*x = (1/x)*x NOT 1/(x*x).
More ...
Press <Pg Dn> to go on. Press <ESC> if finished.
If you want to create a function like
sin(x)/x if x
f(x) =
1 if x = 0
then use the following construction
ifne(x,0,1){sin(x)/x}
which can be read "if x is not equal to 0, use sin(x)/x else use 1".
Similarly,
ifl(x,1){x*x} is x*x if x < 1, and 0 otherwise. ("if less than")
ifle(x,1){x*x} is x*x if x
1, and 0 otherwise. ("if less than or =")
ifg(x,1){x*x} is x*x if x > 1, and 0 otherwise. ("if greater than")
ifge(x,1){x*x} is x*x if x
1, and 0 otherwise. ("if greater than or =")
ifb(x,1,2){x*x} is x*x if 1 < x < 2, and 0 otherwise. ("if between")
ifbe(x,1,2){x*x} is x*x if 1
2, and 0 otherwise. ("if between or =")
These can be combined, so that, for example
ifb(x,1,2){x*x}+ifne(x,2,4){0} is x*x if 1 < x
2, and 0 otherwise.
No more.
Press <Pg Up> to go back. Press <ESC> if finished.
This will allow previously created projects to be loaded in from disk. Project filenames have the extension PRO.
This is where series solutions,
r 2 3
y = (x - a) (a(0) + a(1)(x - a) + a(2)(x - a) + a(3)(x - a) + ...)
of ordinary differential equations of the type
y' + p(x)y = f(x), subject to the initial condition y = y(x0),
or of the type
y" + p(x)y' + q(x) = f(x),
subject to the initial conditions y = y(x0), y' = y'(x0), can be created, edited, and deleted.
This is where the first 21 numerical values of a(n), viz. a(0), a(1), a(2), ... , a(20) are displayed. The maximum number of decimal places shown is 15.
Use this to edit an existing ODE. Select the ODE to be edited by moving the high lighted bar over the ODE and pressing RETURN or ENTER.
This is where you select the domain (x-values) and range (y-values) to be plotted.
This allows you to delete ODEs already created.
To delete an ODE, place the high lighted bar over it, and press ENTER or RETURN.
If you press ESCAPE, no ODEs will be deleted.
This is where you can select the range and domain, the values of the parameters a, b, and c, and where you can plot the functions.
This is where ordinary differential equations of the type
y' + p(x)y = f(x),
subject to the initial condition
y = y(x0),
or of the type
y" + p(x)y' + q(x)y = f(x),
subject to the initial conditions
y = y(x0), y' = y'(x0),
can be created, edited, and deleted.
This allows you to delete series already created.
To delete a series, place the high lighted bar over it, and press RETURN or ENTER.
If you press ESCAPE, no series will be deleted.
Use this to edit an existing series. Select the series to be edited by moving the high lighted bar over the function and pressing RETURN.
This is where a previously created ODE, solution, and/or series can be plotted using your domain and range.
The method used to plot the ODE is Runge-Kutta 4 with adaptive stepsize control. It starts with your intial values and then plots either in the positive direction (P), or in the negative direction (N), depending on what you select. For each of these directions there are three choices.
(1) Plot the numerical values, indicating them with crosses.
(2) Plot the numerical values, indicating them with dots, and join the dots with straight lines.
(3) Plot the numerical values, indicating them with dots, and join the dots by means of cubic splines.
For many ODEs, there is no appreciable graphical difference between (2) and (3), so (2) would be the option of choice, because it is faster than (3). However, if your curve looks choppy, you might want to use option (3).
For positive directions, the keys to press are "P" for (1), "p" for (2), and "ALT p" for (3).
For negative directions, the keys to press are "N" for (1), "n" for (2), and "ALT n" for (3). More ...
Press <Pg Dn> to go on. Press <ESC> if finished.
When the graphics screen appears, the following keys are active.
The "a"/"A" key decreases/increases the value of a by ai.
The "b"/"B" key decreases/increases the value of b by bi.
The "c"/"C" key decreases/increases the value of c by ci.
The "y"/"Y" key decreases/increases the value of y by yi.
The "d"/"D" key decreases/increases the value of dy by dyi.
The "END"/"HOME" key decreases/increases "ai" by a factor of 10.
The "DN ARROW"/"UP ARROW" key decreases/increases "bi" by a factor of 10.
The "PgDn"/"PgUp" key decreases/increases "ci" by a factor of 10.
The "CTRL END"/"CTRL HOME" key decreases/increases "yi" by a factor of 10.
The "CTRL PgDn"/"CTRL PgUp" key decreases/increases "dyi" by a factor of 10.
The "s" key graphs your solution function, s(x).
The "p"/"P"/"ALT p" key tries to graph the numerical solution of your ODE in the positive direction from your initial point.
The "n"/"N"/"ALT n" key tries to graph the numerical solution of your ODE in the negative direction from your initial point.
The "x" key puts a block at the initial position (x0, y0).
More ...
Press <Pg Dn> to go on, <Pg Up> to go back, and <ESC> if finished.
When the graphics screen appears, the following keys are also active.
The "1" key plots your series solution up to the 1st power of (x - a).
The "2" key plots your series solution up to the 2nd of (x - a).
The "9" key plots your series solution up to the 9th power of (x - a).
The "0" key plots your series solution up to the 10th power of (x - a).
The "!" (SHIFT 1) key plots your series solution up to the 11th power.
The "@" (SHIFT 2) key plots your series solution up to the 12th power.
The "(" (SHIFT 9) key plots your series solution up to the 19th power.
The ")" (SHIFT 0) key plots your series solution up to the 20th power.
The "t" key prints the screen to your printer. The type of printer (Epson, IBM PROPRINTER or Laserjet) is selected under the Other Ops menu.
The "v" key puts a movable cross hair at the center of the screen, and shows its coordinates. "+" moves in big steps, "-" in small steps.
The "r" key refreshes the screen.
The ESCAPE key returns you to the main menu.
No more.
Press <Pg Up> to go back. Press <ESC> if finished.
Use this to create functions s(x) which represent solutions of ordinary differential equations of the type
y' + p(x)y = f(x), subject to y = y(x0),
y" + p(x)y' + q(x)y = f(x), subject to y = y(x0), y' = y'(x0).
The function s(x) may include parameters a, b, and c. Up to 10 functions can be created. Of course, s(x) could be any function - it doesn't have to be the solution.
If you press the INSERT key while creating s(x), a list of functions is displayed. You can use and edit these, or create your own functions from scratch.
There are a few points to remember.
Exponentiation is represented by the "^" key, so that 10^2 = 100.
Also x^3/2 = (x^3)/2, NOT x^(3/2).
Finally 1/x*x = (1/x)*x NOT 1/(x*x).
More ...
Press <Pg Dn> to go on. Press <ESC> if finished.
If you want to create a function like
sin(x)/x if x
f(x) =
1 if x = 0
then use the following construction
ifne(x,0,1){sin(x)/x}
which can be read "if x is not equal to 0, use sin(x)/x else use 1".
Similarly,
ifl(x,1){x*x} is x*x if x < 1, and 0 otherwise. ("if less than")
ifle(x,1){x*x} is x*x if x
1, and 0 otherwise. ("if less than or =")
ifg(x,1){x*x} is x*x if x > 1, and 0 otherwise. ("if greater than")
ifge(x,1){x*x} is x*x if x
1, and 0 otherwise. ("if greater than or =")
ifb(x,1,2){x*x} is x*x if 1 < x < 2, and 0 otherwise. ("if between")
ifbe(x,1,2){x*x} is x*x if 1
2, and 0 otherwise. ("if between or =")
These can be combined, so that, for example
ifb(x,1,2){x*x}+ifne(x,2,4){0} is x*x if 1 < x
2, and 0 otherwise.
No more.
Press <Pg Up> to go back. Press <ESC> if finished.
Allows you to load previously saved functions from disk.
Allows you to save created functions to disk.
Allows you to change disk drives.
Allows you to change directories on the current drive.
Gives various disk information, viz. the current drive, the current directory, and the total and remaining free space on the current drive.
Lists all the files in the current directory.
This allows you to identify the graphics printer hooked up to your system. The choice is simple - either EPSON compatible, IBM PROPRINTER, or LASERJET.
If a file named PRINTER.CFG is found, and the contents of the first line of that file is the single word LASER, then the default will be the LASERJET, if the word is IBM, then the default will be the PROPRINTER, otherwise it will be the EPSON.
These are the instructions you should have read when you first ran the program.
The wonderful band of people who don't get enough recognition.
Kwa Heri.
(Swahili for "Good Bye"!)
Use this to edit an existing solution. Select the solution to be edited by moving the high lighted bar over the solution and pressing RETURN or ENTER.
This allows you to delete solutions already created.
To delete a solution, place the high lighted bar over it, and press ENTER or RETURN.
If you press ESCAPE, no solutions will be deleted.
This is where functions are saved and loaded, and other disk oriented chores are performed.
Miscellaneous operations which don't belong anywhere else.
This is where solutions, s(x), of ordinary differential equations of the type
y' + p(x)y = f(x),
subject to the initial condition
y = y(x0),
or of the type
y" + p(x)y' + q(x) = f(x),
subject to the initial condition
y = y(x0), y' = y'(x0),
can be created, edited, and deleted.
This is where you can select new values for the parameters a, b, and c.
Use this to create 1st order ordinary differential equations of the type
y' + p(x)y = f(x),
subject to the initial condition
y = y(x0).
The functions p(x) and f(x) may include parameters a, b, and c. Up to 10 ODEs can be created.
If you press the INSERT key while creating p(x) and f(x), a list of functions is displayed. You can use and edit these, or create your own functions from scratch. You will also be expected to supply the point x0, and the initial value y(x0).
There are a few points to remember.
Exponentiation is represented by the "^" key, so that 10^2 = 100.
Also x^3/2 = (x^3)/2, NOT x^(3/2).
Finally 1/x*x = (1/x)*x NOT 1/(x*x).
More ...
Press <Pg Dn> to go on. Press <ESC> if finished.
If you want to create a function like
sin(x)/x if x
f(x) =
1 if x = 0
then use the following construction
ifne(x,0,1){sin(x)/x}
which can be read "if x is not equal to 0, use sin(x)/x else use 1".
Similarly,
ifl(x,1){x*x} is x*x if x < 1, and 0 otherwise. ("if less than")
ifle(x,1){x*x} is x*x if x
1, and 0 otherwise. ("if less than or =")
ifg(x,1){x*x} is x*x if x > 1, and 0 otherwise. ("if greater than")
ifge(x,1){x*x} is x*x if x
1, and 0 otherwise. ("if greater than or =")
ifb(x,1,2){x*x} is x*x if 1 < x < 2, and 0 otherwise. ("if between")
ifbe(x,1,2){x*x} is x*x if 1
2, and 0 otherwise. ("if between or =")
These can be combined, so that, for example
ifb(x,1,2){x*x}+ifne(x,2,4){0} is x*x if 1 < x
2, and 0 otherwise.
No more.
Press <Pg Up> to go back. Press <ESC> if finished.
Use this to create series of the type
r 2 3
y = (x - a) (a(0) + a(1)(x - a) + a(2)(x - a) + a(3)(x - a) + ...)
by defining a(n) explicitly as a function of n. Up to 10 series can be created. The function a(n) may contain parameters a, b, and c.
If you press the INSERT key while creating a(n), a list of functions is displayed. You can use and edit these, or create your own functions from scratch. You will also be expected to supply the power r, and the point a
about which the function is expanded.
There are a few points to remember.
Exponentiation is represented by the "^" key, so that 10^2 = 100.
Also n^3/2 = (n^3)/2, NOT n^(3/2), and 1/n*n = (1/n)*n NOT 1/(n*n).
If you want to use n!, use the function fac(n).
More ...
Press <Pg Dn> to go on. Press <ESC> if finished.
If you want to create a function like
1/n if n
f(n) =
1 if n = 0
then use the following construction
ifne(n,0,1){1/n}
which can be read "if n is not equal to 0, use 1/n else use 1". Similarly,
ifl(n,2){n*n} is n*n if n < 2, and 0 otherwise. ("if less than")
ifle(n,2){n*n} is n*n if n
2, and 0 otherwise. ("if less than or =")
ifg(n,2){n*n} is n*n if n > 2, and 0 otherwise. ("if greater than")
ifge(n,2){n*n} is n*n if n
2, and 0 otherwise. ("if greater than or =")
ifb(n,2,5){n*n} is n*n if 2 < n < 5, and 0 otherwise. ("if between")
ifbe(n,2,5){n*n} is n*n if 2
5, and 0 otherwise. ("if between or =")
It is sometimes useful to know that:
cos(n*
/2) is zero if n is odd, and otherwise alternates in sign.
sin(n*
/2) is zero if n is even, and otherwise alternates in sign.
No more.
Press <Pg Up> to go back. Press <ESC> if finished.
Use this to create series of the type
r 2 3
y = (x - a) (a(0) + a(1)(x - a) + a(2)(x - a) + a(3)(x - a) + ...)
by defining a(n) in terms of a recurrence relation. Up to 10 series can be created. The program allows you to construct 2nd, 3rd, 4th, and 5th order recurrence relations (valid for n
So, for example, in the case of the 3rd order recurrence relation, you will be expected to supply the coefficients of a(n+1) and a(n), viz. f2(n) and f1(n), together with the initial values for a(0) and a(1). The functions f1, f2, f3, and f4 may contain parameters a, b, and c.
If you press the INSERT key while creating the coefficiients, a list of functions is displayed. You can use and edit these, or create your own functions from scratch. You will also be expected to supply the power r, and the point a about which the function is expanded.
Press <Pg Dn> to go on. Press <ESC> if finished.
If you want to create a function like
1/n if n
f(n) =
1 if n = 0
then use the following construction
ifne(n,0,1){1/n}
which can be read "if n is not equal to 0, use 1/n else use 1". Similarly,
ifl(n,2){n*n} is n*n if n < 2, and 0 otherwise. ("if less than")
ifle(n,2){n*n} is n*n if n
2, and 0 otherwise. ("if less than or =")
ifg(n,2){n*n} is n*n if n > 2, and 0 otherwise. ("if greater than")
ifge(n,2){n*n} is n*n if n
2, and 0 otherwise. ("if greater than or =")
ifb(n,2,5){n*n} is n*n if 2 < n < 5, and 0 otherwise. ("if between")
ifbe(n,2,5){n*n} is n*n if 2
5, and 0 otherwise. ("if between or =")
It is sometimes useful to know that:
cos(n*
/2) is zero if n is odd, and otherwise alternates in sign.
sin(n*
/2) is zero if n is even, and otherwise alternates in sign.
No more.
Press <Pg Up> to go back. Press <ESC> if finished.
When the program plots a solution, it generally starts at the left hand side of the screen, plots a value, moves over an "increment" number of pixels, plots another value, and joins them with a straight line. The smaller the increment, the more accurate the graph, but the longer the time taken to draw it. This option allows you to change the increment from the default value of 5 to a number between 1 and 10.
(.txt)