As indicated above, the TIME menu provides four different options, numbered 1 through 4. Of interest to us as this point is option 3. Set time, date. Using the down arrow key, , highlight this option and press the !!@@OK#@ F soft menu key. The following input form (see Appendix 1-A) for adjusting time and date is shown:
Setting the time of the day Using the number keys, 1234567890, start by adjusting the hour of the day. Suppose that we change the hour to 11, by pressing 11 as the hour field in the SET TIME AND DATE input form is highlighted. This results in the number 11 being entered in the lower line of the input form:
Press the !!@@OK#@ F soft menu key to effect the change. The value of 11 is now shown in the hour field, and the minute field is automatically highlighted:

Page 1-8

Lets change the minute field to 25, by pressing: 25 !!@@OK#@. The seconds field is now highlighted. Suppose that you want to change the seconds field to 45, use: 45 !!@@OK#@ The time format field is now highlighted. To change this field from its current setting you can either press the W key (the second key from the left in the fifth row of keys from the bottom of the keyboard), or press the @CHOOS soft menu key ( B). If using the W key, the setting in the time format field will change to either of the following options: o o o AM : indicates that displayed time is AM time PM : indicates that displayed time is PM time 24-hr : indicates that that the time displayed uses a 24 hour format where18:00, for example, represents 6pm
The last selected option will become the set option for the time format by using this procedure. If using the @CHOOS soft menu key, the following options are available.
Use the up and down arrow keys, , to select among these three options (AM, PM, 24-hour time). Press the !!@@OK#@ F soft menu key to make the selection. Setting the date After setting the time format option, the SET TIME AND DATE input form will look as follows:

Page 1-9

To set the date, first set the date format. The default format is M/D/Y (month/day/year). To modify this format, press the down arrow key. This will highlight the date format as shown below:
Use the @CHOOS soft menu key ( B), to see the options for the date format:
Highlight your choice by using the up and down arrow keys, , and press the !!@@OK#@ F soft menu key to make the selection.
Introducing the calculators keyboard
The figure below shows a diagram of the calculators keyboard with the numbering of its rows and columns.

Page 1-10

The figure shows 10 rows of keys combined with 3, 5, or 6 columns. Row 1 has 6 keys, rows 2 and 3 have 3 keys each, and rows 4 through 10 have 5 keys each. There are 4 arrow keys located on the right-hand side of the keyboard in the space occupied by rows 2 and 3. Each key has three, four, or five functions. The main key function correspond to the most prominent label in the key. Also, the green left-shift key, key (8,1), the red right-shift key, key (9,1), and the blue ALPHA key, key (7,1), can be

Page 2-66

The HELP menu, activated with I L @HELP
The CMDS (CoMmanDS) menu, activated within the Equation Writer, i.e., O L @CMDS

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Chapter 3 Calculation with real numbers
This chapter demonstrates the use of the calculator for operations and functions related to real numbers. Operations along these lines are useful for most common calculations in the physical sciences and engineering. The user should be acquainted with the keyboard to identify certain functions available in the keyboard (e.g., SIN, COS, TAN, etc.). Also, it is assumed that the reader knows how to adjust the calculator's operation, i.e., select operating mode (see Chapter 1), use menus and choose boxes (see Chapter 1), and operate with variables (see Chapter 2).
Checking calculators settings
To check the current calculator and CAS settings you need to just look at the top line in the calculator display in normal operation. For example, you may see the following setting: RAD XYZ DEC R = X This stands for RADians for angular measurements, XYZ for Rectangular (Cartesian) coordinates, DECimal number base, Real numbers preferred, = means exact results, and X is the value of the default independent variable. Another possible listing of options could be DEG RZ HEX C ~ t
This stands for DEGrees as angular measurements, RZ for Polar coordinates, HEXagesimal number base, Complex numbers allowed, ~ stands for approximate results, and t as the default independent variable. In general, this part of the display contains seven elements. Each element is identified next under numbers 1 through 7. The possible values for each element are shown between parentheses following the element description. The explanation of each of those values is also shown: 1. Angle measure specification (DEG, RAD, GRD) DEG: degrees, 360 degrees in a complete circle RAD: radians, 2 radians in a complete circle GRD: grades, 400 grades in a complete circle

Page 3-1

2. Coordinate system specification (XYZ, RZ, R). stands for an angular coordinate. XYZ: Cartesian or rectangular (x,y,z) RZ: cylindrical Polar coordinates (r,,z) R: Spherical coordinates (,,) 3. Number base specification (HEX, DEC, OCT, BIN) HEX: hexadecimal numbers (base 16) DEC: decimal numbers (base 10) OCT: octal numbers (base 8) BIN: binary numbers (base 2) 4. Real or complex mode specification (R, C) R: real numbers C: complex numbers 5. Exact or approximate mode specification (=, ~) = exact (symbolic) mode ~ approximate (numerical) mode 6. Default CAS independent variable (e.g., X, t, etc.)

The symbol

Checking calculator mode
When in RPN mode the different levels of the stack are listed in the left-hand side of the screen. When the ALGEBRAIC mode is selected there are no numbered stack levels, and the word ALG is listed in the top line of the display towards the right-hand side. The difference between these operating modes was described in detail in Chapter 1.

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ENERGY J (joule), erg (erg), Kcal (kilocalorie), Cal (calorie), Btu (International table btu), ftlbf (foot-pound), therm (EEC therm), MeV (mega electron-volt), eV (electronvolt) POWER W (watt), hp (horse power), PRESSURE Pa (pascal), atm (atmosphere), bar (bar), psi (pounds per square inch), torr (torr), mmHg (millimeters of mercury), inHg (inches of mercury), inH20 (inches of water), TEMPERATURE C (degree Celsius), o F (degree Fahrenheit), K (Kelvin), o R (degree Rankine), ELECTRIC CURRENT (Electric measurements) V (volt), A (ampere), C (coulomb), (ohm), F (farad), W (watt), Fdy (faraday), H (henry), mho (mho), S (siemens), T (tesla), Wb (weber ) ANGLE (planar and solid angle measurements) (sexagesimal degree), r (radian), grad (grade), arcmin (minute of arc), arcs (second of arc), sr (steradian)
LIGHT (Illumination measurements) fc (footcandle), flam (footlambert), lx (lux), ph (phot), sb (stilb), lm (lumem), cd (candela), lam (lambert) RADIATION Gy (gray), rad (rad), rem (rem), Sv (sievert), Bq (becquerel), Ci (curie), R (roentgen) VISCOSITY P (poise), St (stokes)

Page 3-20

Units not listed Units not listed in the Units menu, but available in the calculator include: gmol (gram-mole), lbmol (pound-mole), rpm (revolutions per minute), dB (decibels). These units are accessible through menu 117.02, triggered by using MENU(117.02) in ALG mode, or 117.02 ` MENU in RPN mode. The menu will show in the screen as follows (use to show labels in display):
These units are also accessible through the catalog, for example: gmol: lbmol: rpm: dB: N~g N~l N~r N~d

Converting to base units

To convert any of these units to the default units in the SI system, use the function UBASE. For example, to find out what is the value of 1 poise (unit of viscosity) in the SI units, use the following: In ALG mode, system flag 117 set to CHOOSE boxes: Select the UNITS menu @@OK@@ Select the TOOLS menu @@OK@@ Select the UBASE function 1 Enter 1 and underline Select the UNITS menu @@OK@@ Select the VISCOSITY option @@OK@@ Select the UNITS menu ` Convert the units

J @@@n@@ @IYR@ @@PV@@ @@PMT@@ @@PYR@@ @@FV@@ ` I@PURGE
Prepare a list of variables to be purged Enter name of variable N Enter name of variable I%YR Enter name of variable PV Enter name of variable PMT Enter name of variable PYR Enter name of variable FV Enter list of variables in stack Purge variables in list
Before the command PURGE is entered, the RPN stack will look like this:
Solving equations with one unknown through NUM.SLV
The calculator's NUM.SLV menu provides item 1. Solve equation. solve different types of equations in a single variable, including non-linear algebraic and transcendental equations. For example, let's solve the equation: exsin(x/3) = 0. Simply enter the expression as an algebraic object and store it into variable EQ. The required keystrokes in ALG mode are the following: ~x-S *~x/K~e~q` Function STEQ Function STEQ, available through the command catalog, N, will store its argument into variable EQ, e.g., in ALG mode:
In RPN mode, enter the equation between apostrophes and activate command STEQ. Thus, function STEQ can be used as a shortcut to store an expression into variable EQ.

Page 6-14

Press J to see the newly created EQ variable:
Then, enter the SOLVE environment and select Solve equation, by using: @@OK@@. The corresponding screen will be shown as:
The equation we stored in variable EQ is already loaded in the Eq field in the SOLVE EQUATION input form. Also, a field labeled x is provided. To solve the equation all you need to do is highlight the field in front of X: by using , and press @SOLVE@. The solution shown is X: 4.5006E-2:
This, however, is not the only possible solution for this equation. To obtain a negative solution, for example, enter a negative number in the X: field before solving the equation. Try 3\@@@OK@@@SOLVE@. The solution is now X: 3.045. Solution procedure for Equation Solve. The numerical solver for single-unknown equations works as follows: It lets the user type in or @CHOOS an equation to solve. It creates an input form with input fields corresponding to all variables involved in equation stored in variable EQ. The user needs to enter values for all variables involved, except one.

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Under-determined system The system of linear equations 2x1 + 3x2 5x3 = -10, x1 3x2 + 8x3 = 85, can be written as the matrix equation Ax = b, if
x A= , x = x2 , and 8 x3

10 b=. 85

This system has more unknowns than equations, therefore, it is not uniquely determined. We can visualize the meaning of this statement by realizing that each of the linear equations represents a plane in the three-dimensional Cartesian coordinate system (x1, x2, x3). The solution to the system of equations shown above will be the intersection of two planes in space. We know, however, that the intersection of two (non-parallel) planes is a straight line, and not a single point. Therefore, there is more than one point that satisfy the system. In that sense, the system is not uniquely determined. Lets use the numerical solver to attempt a solution to this system of equations: @@OK@@. Enter matrix A and vector b as illustrated in the previous example, and press @SOLVE when the X: field is highlighted:

Page 11-19

To see the details of the solution vector, if needed, press the @EDIT! button. This will activate the Matrix Writer. Within this environment, use the rightand left-arrow keys to move about the vector, e.g.,
Thus, the solution is x = [15.373, 2.4626, 9.6268]. To return to the numerical solver environment, press `. The procedure that we describe next can be used to copy the matrix A and the solution vector X into the stack. To check that the solution is correct, try the following: Press Press Press Press Press Press , to highlight the A: field. L @CALC@ `, to copy matrix A onto the stack. @@@OK@@@ to return to the numerical solver environment. @CALC@ `, to copy solution vector X onto the stack. @@@OK@@@ to return to the numerical solver environment. ` to return to the stack.
In ALG mode, the stack will now look like this:

Page 11-20

Lets store the latest result in a variable X, and the matrix into variable A, as follows: Press K~x` to store the solution vector into variable X Press to clear three levels of the stack Press K~a` to store the matrix into variable A Now, lets verify the solution by using: @@@A@@@ * @@@X@@@ `, which results in (press to see the vector elements): [-9.99999999999 85. ], close enough to the original vector b = [-10 85]. Try also this, @@A@@@ * [15,10/3,10] ` `, i.e.,
This result indicates that x = [15,10/3,10] is also a solution to the system, confirming our observation that a system with more unknowns than equations is not uniquely determined (under-determined). How does the calculator came up with the solution x = [15.37 2.46 9.62] shown earlier? Actually, the calculator minimizes the distance from a point, which will constitute the solution, to each of the planes represented by the equations in the linear system. The calculator uses a least-square method, i.e., minimizes the sum of the squares of those distances or errors. Over-determined system The system of linear equations x1 + 3x2 = 15, 2x1 5x2 = 5, -x1 + x2 = 22,

Graph of the exponential function
First, load the function exp(X), by pressing, simultaneously if in RPN mode, the left-shift key and the (V) key to access the PLOT-FUNCTION window. Press @@DEL@@ to remove the function LN(X), if you didnt delete Y1 as suggested in the previous note. Press @@ADD@! and type ~x` to enter EXP(X) and return to the PLOT-FUNCTION window. Press L@@@OK@@@ to return to normal calculator display. Next, press, simultaneously if in RPN mode, the left-shift key and the (B) key to produce the PLOT WINDOW - FUNCTION window. Change the H-View values to read: H-View: -by using 8\@@@OK@@ @2@@@OK@@@. Next, press @AUTO. After the vertical range is calculated, press @ERASE @DRAW to plot the exponential function.

Page 12-10

To add labels to the graph press @EDIT L@)LABEL. Press @MENU to remove the menu labels, and get a full view of the graph. Press LL@)PICT! @CANCL to return to the PLOT WINDOW FUNCTION. Press ` to return to normal calculator display.

The PPAR variable

Press J to recover your variables menu, if needed. In your variables menu you should have a variable labeled PPAR. Press @PPAR to get the contents of this variable in the stack. Press the down-arrow key, , to launch the stack editor, and use the up- and down-arrow keys to view the full contents of PPAR. The screen will show the following values:
PPAR stands for Plot PARameters, and its contents include two ordered pairs of real numbers, (-8.,-1.10797263281) and (2.,7.38905609893), which represent the coordinates of the lower left corner and the upper right corner of the plot, respectively. Next, PPAR lists the name of the independent variable, X, followed by a number that specifies the increment of the independent variable in the generation of the plot. The value shown here is the default value, zero (0.), which specifies increments in X corresponding to 1 pixel in the graphics display. The next element in PPAR is a list containing first the coordinates of the point of intersection of the plot axes, i.e., (0.,0.), followed by a list that specifies the tick mark annotation on the x- and y-axes, respectively {# 10d # 10d}. Next, PPAR lists the type of plot that is to be generated, i.e., FUNCTION, and, finally, the y-axis label, i.e., Y. The variable PPAR, if non-existent, is generated every time you create a plot. The contents of the function will change depending on the type of plot and on the options that you select in the PLOT window (the window generated by the simultaneous activation of the and (B) keys.

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Inverse functions and their graphs

To recover the menu and return to the PLOT environment, press L@CANCL. To return to normal calculator display, press L@@@OK@@@.

Parametric plots

Parametric plots in the plane are those plots whose coordinates are generated through the system of equations x = x(t) and y = y(t), where t is known as the parameter. An example of such graph is the trajectory of a projectile, x(t) = x0 + v0COS 0t, y(t) = y0 + v0sin 0t gt2. To plot equations like these, which involve constant values x0, y0, v0, and 0, we need to store the values of those parameters in variables. To develop this example, create a subdirectory called PROJM for PROJectile Motion, and within that sub-directory store the following variables: X0 = 0, Y0 = 10, V0 = 10 , 0 = 30, and g = 9.806. Make sure that the calculators angle measure is set to DEG. Next, define the functions (use ):

Page 12-23

X(t) = X0 + V0*COS(0)*t Y(t) = Y0 + V0*SIN(0)*t 0.5*g*t^2 which will add the variables @@@Y@@@ and @@@X@@@ to the soft menu key labels.
To produce the graph itself, follow these steps: Press , simultaneously if in RPN mode, to access to the PLOT SETUP window. Change TYPE to Parametric, by pressing @CHOOS @@@OK@@@. Press and type X(t) + i*Y(t) @@@OK@@@ to define the parametric plot as that of a complex variable. (The real and imaginary parts of the complex variable correspond to the x- and y-coordinates of the curve.) The cursor is now in the Indep field. Press ~t @@@OK@@@ to change the independent variable to t. Press L@@@OK@@@ to return to normal calculator display. Press , simultaneously if in RPN mode, to access the PLOT window (in this case it will be called PLOT PARAMETRIC window). Instead of modifying the horizontal and vertical views first, as done for other types of plot, we will set the lower and upper values of the independent variable first as follows: Select the Indep Low field by pressing. Change this value to 0@@@OK@@@. Then, change the value of High to 2@@@OK@@@. Enter 0. 1@@@OK@@@ for the Step value (i.e., step = 0.1). Note: Through these settings we are indicating that the parameter t will take values of t = 0, 0.1, 0.2, , etc., until reaching the value of 2.0. Press @AUTO. This will generate automatic values of the H-View and V-View ranges based on the values of the independent variable t and the definitions of X(t) and Y(t) used. The result will be:

Page 12-24

Press @ERASE @DRAW to draw the parametric plot. Press @EDIT L @LABEL @MENU to see the graph with labels. The window parameters are such that you only see half of the labels in the x-axis.

2 - An equivalent value of the function near x = a 3 - Expression for the Taylor polynomial 4 - Order of the residual or remainder Because of the relatively large amount of output, this function is easier to handle in RPN mode. For example:
Drop the contents of stack level 1 by pressing , and then enter , to decompose the list. The results are as follows:

Page 13-25

In the right-hand side figure above, we are using the line editor to see the series expansion in detail.

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Chapter 14 Multi-variate Calculus Applications
Multi-variate calculus refers to functions of two or more variables. In this Chapter we discuss the basic concepts of multi-variate calculus including partial derivatives and multiple integrals.

Multi-variate functions

A function of two or more variables can be defined in the calculator by using the DEFINE function (). To illustrate the concept of partial derivative, we will define a couple of multi-variate functions, f(x,y) = x cos(y), and g(x,y,z) = (x2+y2)1/2sin(z), as follows:
We can evaluate the functions as we would evaluate any other calculator function, e.g.,
Graphics of two-dimensional functions are possible using Fast3D, Wireframe, Ps-Contour, Y-Slice, Gridmap, and Pr-Surface plots as described in Chapter 12.

Partial derivatives

Consider the function of two variables z = f(x,y), the partial derivative of the function with respect to x is defined by the limit

Page 14-1

f ( x + h, y ) f ( x , y ) f. = lim h 0 h x

Similarly,

f f ( x, y + k ) f ( x, y ) = lim. k 0 y k
We will use the multi-variate functions defined earlier to calculate partial derivatives using these definitions. Here are the derivatives of f(x,y) with respect to x and y, respectively:
Notice that the definition of partial derivative with respect to x, for example, requires that we keep y fixed while taking the limit as h 0. This suggest a way to quickly calculate partial derivatives of multi-variate functions: use the rules of ordinary derivatives with respect to the variable of interest, while considering all other variables as constant. Thus, for example,
(x cos( y ) ) = cos( y ), (x cos( y ) ) = x sin( y ) , x y

Beta pdf:

' pdf(x)= GAMMA(+)*x^(-1)*(1-x)^(-1)/(GAMMA()*GAMMA())' Beta cdf: ' cdf(x) = (0,x, pdf(t),t)' Exponential pdf: 'epdf(x) = EXP(-x/)/' Exponential cdf: 'ecdf(x) = 1 - EXP(-x/)' Weibull pdf: 'Wpdf(x) = **x^(-1)*EXP(-*x^)' Weibull cdf: 'Wcdf(x) = 1 - EXP(-*x^)'
Use function DEFINE to define all these functions. Next, enter the values of and , e.g., 1K~a` 2K ~b` Finally, for the cdf for Gamma and Beta cdfs, you need to edit the program definitions to add NUM to the programs produced by function DEFINE. For example, the Gamma cdf, i.e., the function gcdf, should be modified to read: x ' NUM( (0,x,gpdf(t),t))' and stored back into @gcdf. Repeat the procedure for cdf. Unlike the discrete functions defined earlier, the continuous functions defined in this section do not include their parameters ( and/or ) in their definitions. Therefore, you don't need to enter them in the display to calculate the functions. However, those parameters must be previously defined by storing the corresponding values in the variables and. Once all functions and the values and have been stored, you can order the menu labels by using function ORDER. The call to the function will be the following: ORDER({,,gpdf,gcdf,pdf,cdf,epdf,ecdf,Wpdf,Wcdf}) Following this command the menu labels will show as follows (Press L to move to the second list. Press L once more to move to the first list):

Page 17-8

Some examples of application of these functions, for values of = 2, = 3, are shown below. Notice the variable IERR that shows up in the second screen shot. This results from a numerical integration for function gcdf.
Continuous distributions for statistical inference
In this section we discuss four continuous probability distributions that are commonly used for problems related to statistical inference. These distributions are the normal distribution, the Students t distribution, the Chisquare (2) distribution, and the F-distribution. The functions provided by the calculator to evaluate probabilities for these distributions are contained in the MTH/PROBABILITY menu introduced earlier in this chapter. The functions are NDIST, UTPN, UTPT, UTPC, and UTPF. Their application is described in the following sections. To see these functions activate the MTH menu: and select the PROBABILITY option:

Enter a 2 and multiply it with g (by)2
Swap Q with 2g (by)2 Square Q Swap 2g (by)2 with Q2 Divide Q2 by 2g (by)2 Enter the program
The resulting program looks like this: * SQ * 2 * SWAP SQ SWAP /

Page 21-18

Note: SQ is the function that results from the keystroke sequence. Save the program into a variable called hv: ~h~v K A new variable @@@hv@@@ should be available in your soft key menu. (Press J to see your variable list.) The program left in the stack can be evaluated by using function EVAL. The result should be 0.228174, as before. Also, the program is available for future use in variable @@@hv@@@. For example, for Q = 0.5 m3/s, g = 9.806 m/s2, b = 1.5 m, and y = 0.5 m, use: 0.5 # 9.806 #1.5 # 0.5 @@@hv@@@ Note: #is used here as an alternative to ` for input data entry. The result now is 2.26618623518E-2, i.e., hv = 2.2661862351810-2 m. Note: Since the equation programmed in @@@hv@@@ is dimensionally consistent, we can use units in the input. As mentioned earlier, the two types of programs presented in this section are sequential programs, in the sense that the program flow follows a single path, i.e., INPUT OPERATION OUTPUT. Branching of the program flow is possible by using the commands in the menu @)@BRCH@. More detail on program branching is presented below.
Interactive input in programs
In the sequential program examples shown in the previous section it is not always clear to the user the order in which the variables must be placed in the stack before program execution. For the case of the program @@@q@@@, written as
Cu n y0 S0 Cu/n*y0^(5/3)*S0

Page 21-19

it is always possible to recall the program definition into the stack (@@@q@@@) to see the order in which the variables must be entered, namely, Cu n y0 S0. However, for the case of the program @@hv@@, its definition * SQ * 2 * SWAP SQ SWAP / does not provide a clue of the order in which the data must be entered, unless, of course, you are extremely experienced with RPN and the User RPL language. One way to check the result of the program as a formula is to enter symbolic variables, instead of numeric results, in the stack, and let the program operate on those variables. For this approach to be effective the calculators CAS (Calculator Algebraic System) must be set to symbolic and exact modes. This is accomplished by using H@)CAS@, and ensuring that the check marks in the options _Numeric and _Approx are removed. Press @@OK@@ @@OK@ to return to normal calculator display. Press J to display your variables menu. We will use this latter approach to check what formula results from using the program @@hv@@ as follows: We know that there are four inputs to the program, thus, we use the symbolic variables S4, S3, S2, and S1 to indicate the stack levels at input: ~s4` ~s3` ~s2` ~s1`

Page 22-25

correspond to the lower right corner of the screen {# 82h #3Fh}, which in user-coordinates is the point (xmax, ymin). The coordinates of the two other corners both in pixel as well as in user-defined coordinates are shown in the figure.

Animating graphics

Herein we present a way to produce animation by using the Y-Slice plot type. Suppose that you want to animate the traveling wave, f(X,Y) = 2.5 sin(X-Y). We can treat the X as time in the animation producing plots of f(X,Y) vs. Y for different values of X. To produce this graph use the following: simultaneously. Select Y-Slice for TYPE. 2.5*SIN(X-Y) for EQ. X for INDEP. Press L@@@OK@@@. , simultaneously (in RPN mode). Use the following values:
Press @ERASE @DRAW. Allow some time for the calculator to generate all the needed graphics. When ready, it will show a traveling sinusoidal wave in your screen.

Page 22-26

Animating a collection of graphics
The calculator provides the function ANIMATE to animate a number of graphics that have been placed in the stack. You can generate a graph in the graphics screen by using the commands in the PLOT and PICT menus. To place the generated graph in the stack, use PICT RCL. When you have n graphs in levels n through 1 of the stack, you can simply use the command n ANIMATE to produce an animation made of the graphs you placed in the stack. Example 1 Animating a ripple in a water surface As an example, type in the following program that generates 11 graphics showing a circle centered in the middle of the graphics screen and whose radius increase by a constant value in each subsequent graph. RAD 131 R B 64 R B PDIM XRNG YRNG FOR j ERASE (50., 50.) 5*(j-1) NUM 0 2* NUM ARC PICT RCL NEXT 11 ANIMATE Begin program Set angle units to radians Set PICT to 13164 pixels Set x- and y-ranges to 0-100 Start loop with j = 1. 11 Erase current PICT Centers of circles (50,50) Draw circle center r = 5(j-1) Place current PICT on stack End FOR-NEXT loop Animate End program
Store this program in a variable called PANIM (Plot ANIMation). To run the program press J (if needed) @PANIM. It takes the calculator more than one minute to generate the graphs and get the animation going. Therefore, be really patient here. You will see the hourglass symbol up in the screen for what seems a long time before the animation, resembling the ripples produced by a pebble dropped on the surface of a body of quiescent water, appears in the screen. To stop the animation, press $.

GAMMA, 3-15 Gamma distribution, 17-6 GAUSS, 11-53 Gaussian elimination, 11-28 Gauss-Jordan elimination, 11-28 11-37 11-39 GCD, 5-11, 5-19 GCDMOD, 5-12 Geometric mean, 18-3 Geometric mean, 8-16 GET, 10-6 GETI, 8-11 Global variable scope, 21-4 Global variable, 21-2 GOR, 22-32 Goto Line, L-4 GOTO menu, L-2 L-3 Goto Position, L-4 Grades, 1-22 Gradient, 15-1 Graphic objects, 22-30 Graphical solution of ODEs, 16-60 Graphics animation, 22-26 Graphics options, 12-1 Graphics programming, 22-1 Graphs, 12-1 Graphs polar, 12-19 Graphs conic curves, 12-21 Graphs parametric, 12-23
Graphs differential equations, 12-26
Graphs slope fields, 12-34 Graphs Fast 3D plots, 12-35 Graphs wireframe plots, 12-34 Graphs Ps-Contour plots, 12-39 Graphs Y-Slice plots, 12-41 Graphs Gridmap plots, 12-42 Graphs Pr-Surface plots, 12-43 Graphs Zooming, 12-49 Graphs SYMBOLIC menu, 12-51 Graphs saving, 12-7 GRD, 3-1 Greek letters, D-3, G-2 Gridmap plots, 12-42 GROB, 22-30 GROB programming, 22-33 GROB menu, 22-31 GROBADD, 12-52 Grouped data, 8-18 Grouped data statistics, 8-18 Grouped data variance, 8-18 GXOR, 22-32
HADAMARD, 11-5 HALT, L-2 Harmonic mean, 8-15 HEAD, 8-11 Header size, 1-29 Heaviside's step function, 16-15 HELP, 2-26 HERMITE, 5-11, 5-20 Hermite polynomials, 16-60 HESS, 15-2 Hessian matrix, 15-2 HEX, 19-2 HEX, 3-1 Hexadecimal numbers, 19-7
Graphs Graphs Graphs Graphs
truth plots, 12-29 bar plots, 12-30 histograms, 12-30 scatterplots, 12-30

Page M-7

Higher-order derivatives, 13-13 Higher-order partial derivatives, 14-3 HILBERT, 10-14 Histograms, 12-30 HMS-, 25-3 HMS+, 25-3 HMS-->, 25-3 HORNER, 5-11, 5-20 H-VIEW, 12-20 Hyperbolic functions graphs, 1216 Hypothesis testing, 18-34 Hypothesis testing errors, 18-35 Hypothesis testing in linear regression, 18-52 Hypothesis testing in the calculator, 18-42 Hypothesis testing on variances, 18-46 HZIN, 12-50 HZOUT, 12-50
i, 3-16 I/O functions menu, F-2 IR, 5-28 IABCUV, 5-11 IBERNOULLI, 5-11 ICHINREM, 5-11 Identity matrix, 10-1 Identity matrix, 11-6 IDIV2, 5-11 IDN, 10-9 IEGCD, 5-11 IF.THEN.ELSE.END, 21-48
IF.THEN.END, 21-47 IFERR sub-menu, 21-65 IFTE, 3-35 ILAP, 16-11 Illumination units, 3-20 IM, 4-6 IMAGE, 11-54 Imaginary part, 4-1 Implicit derivatives, 13-7 Improper integrals, 13-21 Increasing-power CAS mode, C-9 INDEP, 22-6, Independent variable in CAS, C-2, Infinite series, 13-21, 13-23 INFO, 22-4 INPUT, 21-22 , Input forms programming, 21-21 Input forms use of A-1 Input string prompt programming, 21-21 Input-output functions menu, F-2 INS , L-1 INT, 13-14 Integer numbers, C-5 Integers, 2-1 Integrals, 13-14 Integrals definite, 13-15 Integrals step-by-step, 13-17 Integrals improper, 13-21 Integrals double, 14-6 Integrals multiple, 14-6

Page M-15

Series, 13-23 Series Maclaurin, 13-23 Series Taylor, 13-23 SERIES, 13-23 Series Fourier, 16-27 Setting time and date, 25-2 SHADE in plots, 12-6 Shortcuts, G-1 SI, 3-29 SIGMA, 13-14 SIGMAVX, 13-14 SIGN, 3-14 SIGN, 4-6 SIGNTAB, 12-52 13-10 SIMP2, 5-10, 5-24 SIMPLIFY, 5-29 Simplify non-rational CAS setting, C10 Simplifying an expression, 2-23 SIN, 3-7 Single-variable statistics, 18-2
Singular value decomposition, 11-8
SINH, 3-9 SIZE, 8-10 SIZE, 10-7 SKIP , L-1 SL, 19-6 , SLB, 19-7 Slope fields, 12-34 Slope fields for differential equations, 16-3 SLOPE in plots, 12-7 SNRM, 11-7 SOFT menus, 1-3 SOLVE, 5-5 SOLVE, 6-2, 7-1,
SOLVE menu, 6-27 SOLVE menu (menu 74), G-3 SOLVE/DIFF menu, 16-69 SOLVEVX, 6-4 SOLVR menu, 6-28 SORT, 2-34 Special characters, G-2 Speed units, 3-19 SPHERE, 9-15 SQ, 3-5 Square root, 3-5 Square wave Fourier series 16-39 SR, 19-6 SRAD, 11-9 SRB, 19-7 SREPL, 23-3 SST, 21-35 Stack properties, 1-27 Standard deviation, 18-4 Standard format, 1-17 Standard normal distribution, 1717, START.STEP construct, 21-58 START.NEXT construct, 21-54 STAT menu, 18-15 STAT menu (menu 96), G-3 Statistical inference probability distributions, 17-9 Statistics, 18-1 Step function (Heaviside's ), 16-15 Step-by-step CAS mode, C-7 Step-by-step derivatives, 13-16 Step-by-step integrals, 13-16 STEQ, 6-14 Stiff differential equations, 16-71 Stiff ODE, 16-68

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Stiff ODEs numerical solution, 16-69
Strings, 23-1 STO, 2-46 STOALARM, 25-4 STOKEYS, 20-6 STREAM, 8-12 String concatenation, 23-2 Student t distribution, 17-11 STURM, 5-11 STURMAB, 5-11 STWS, 19-4 Style menu, L-4 SUB, 10-11 Sub-directories creating, 2-38 Sub-directories deleting, 2-42 Sub-expressions, 2-17 SUBST, 5-5 SUBTMOD, 5-12 SUBTMOD, 5-16 Sum of squared errors (SSE), 18-62 Sum of squared totals (SST), 18-62, Summary statistics, 18-13 SVD, 11-50 SVL, 11-50 SYLVESTER, 11-53 SYMB/GRAPH menu, 12-52 Symbolic CAS mode, C-3 SYMBOLIC menu, 12-51 Synthetic division, 5-26, SYST2MAT, 11-42, System flag (EXACT/APPROX), G-1, System flag 117 (CHOOSE/SOFT), 1-4, G-2, System flag 95 (ALG/RPN), G-1
system flags, 24-3 System level operation, G-3 System of equations, 11-16 System tests, G-3
Table, 12-17, 12-26 TABVAL, 12-52, 13-9 TABVAR, 12-52, 13-11 Tagged output programming, 21-34 TAIL, 8-11 TAN, 3-7 TANH, 3-9 Taylor polynomial, 13-23 Taylor series, 13-24 TAYLR, 13-25 TAYLR0, 13-24 TCHEBYCHEFF, 5-24 Tchebycheff polynomials, 16-58 TDELTA, 3-31 Techniques of integration, 13-18 Temperature units, 3-20 TEXPAND, 5-5 Text editor. menu, F-5 Three-dimensional plot programs, 22-15 Three-dimensional vector, 9-13 TICKS, 25-3 Time setting 25-2 TIME, 25-3 Time & date. menu, F-3 Time functions, 25-1 TIME menu, 25-1 Time setting, 1-7 TIME tools, 25-2

hp calculators
HP 48GII Using the Numeric Solver to solve a formula
The Numeric Solver Practice solving formulas for unknowns
hp calculators HP 48GII Using the Numeric Solver to solve a formula The Numeric Solver The HP 48GII has a numeric solver that can find the solutions to many different types of problems. It is invoked by pressing the RED shift key followed by the 7 key, or. When pressed, the CHOOSE box below is displayed:

Figure 1

The first choice allows for the solution of an equation containing a number of unknowns. The second choice solves differential equation problems. The third choice solves for zeroes of a polynomial and is of interest here. The fourth choice can solve linear systems of equations for unknown values. The fifth choice invokes the finance solver. The sixth choice begins the multiple equation solver. To select the equation solver, press `. The 48GII displays the following screen:

Figure 2

There is one input area on this form. This is where equation to be solved is entered. To enter an equation, press !!!EDIT!!.

Figure 3

The cursor will be flashing between the two quote marks at the bottom left corner of the screen. The 48GII is waiting for the entry of an equation. Type in the following:

Figure 4

and press ##OK## shown above the F key at the right side of the display. The equation entered will be stored in the variable EQ in the current directory and will be displayed in the Eq: line of the screen, as shown below. If the variable EQ already contained an equation when the solver was entered, it would have been displayed in the Eq: line in the display above.
hp calculators HP 48GII Using the Numeric Solver to solve a formula

Figure 5

If you prefer, the EquationWriter can be used to type up an equation which is then placed on the stack. If you place the EQ name in the first level of the stack with the equation from the EquationWriter in the second level of the stack and press K, the equation will be stored in the EQ variable. It may be easier to do this before starting the solver for many equations. The remainder of the screen below the Eq: line is where the 48GII solver will place variables found in the equation. Each variable will be given an input space on this screen where you can either input a known value for the variable or attempt to solve for the value of that variable if it is unknown. In the example shown, the only variable is X and there is one entry line for it as shown below.

Figure 6

To solve for the value of X that makes the entered equation equal to zero, press the !!!SOLVE!! menu label above the F key at the right side of the display. The 48GII will solve for X and return its value as shown below.

Figure 7

Note that the solver returned only one of the real solutions to the equation, +2. The solver only finds one answer. To seek for other answers, a starting guess can be given for the variable to influence the search for an answer. It may also be easier to graph the function and look for roots in that manner. Consider what the solver returns if the cursor is placed over the X: input area and 3 is entered followed by pressing the !!!SOLVE!! menu label above the F key at the right side of the display:

Figure 8

The solver found the other real solution to the equation. If you do not have any idea for a possible solution, the solver will make a guess and attempt to find an answer. However, to find other answers, a user-supplied guess may be needed. Practice solving formulas for unknowns Example 1: The equation for the motion of a free-falling object is shown below, where V0 is the initial velocity, T is the time, and G is the acceleration due to gravity.

Figure 9

If an object begins at rest, determine how far the object falls in 5 seconds? How long does it take an object to fall 500 meters? Solution: To answer these questions, use the EquationWriter to enter the function and solve for the unknowns using the numeric solver as shown. Since the answer is to be in meters, use a value of 9.8 m/s2 for G. O~~distv0*t+0.5*g* t~Q2`

Figure 10

~~eq`K`

Figure 11

0`5`9.8`!!!SOLVE!!

Figure 12

500`!!!SOLVE!!

Figure 13

Answer: Example 2:
The object would fall 122.5 meters in 5 seconds. It would take the object a little over 10.1 seconds to fall 500 meters. Given the length of two sides of a triangle and the angle between the two known sides, the length of the third side of the triangle can be determined using the formula shown below:

Figure 14

Given a triangle with Side 1 equal to 170 feet, Side 2 equal to 220 feet, and the included Angle A1 equal to 30 degrees, what is the length of the third side of the triangle? Solution: To answer these questions, use the EquationWriter to enter the function and solve for the unknowns using the numeric solver as shown. Make sure the 48GII is in degrees mode before starting the solver. HCHOOS ##OK## ##OK##

Figure 15

O~s3R~s1Q2+~s2Q2 -2*~s1*~s2*T~a1`

Figure 16

Figure 17

170`220`30`!!!SOLVE!!

Figure 18

Answer:

The third side of the triangle is 111.89 feet in length.