Entering Data In Lists:

1. Press STAT.  Select 1:ENTER

2. Use the left & right scroll buttons to select the list you wish to use.  If data is in the list, clear the list by moving the cursor to the list name, press CLEAR followed by scroll down.

3. Enter the data one value at a time pressing ENTER  between entries.

4. If a new list, not shown, is to be created, scroll to the name bar and press 2nd INS.  A blank list is created.  Enter a name.  
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Plotting Data

1. Enter X and Y data in two respective lists, say L₁ and L₂.  (see  Entering Data In Lists )

2. Press 2nd Y= and make sure all Y_n= signs are un-highlighted.  If any are highlighted, scroll to them and press ENTER.  This prevents functions from being plotted.

3. Press 2nd STAT PLOT.

4. Select any plot by scrolling to it and pressing ENTER.

5. Make sure ON is highlighted.

6. Scroll down to Type: and select the type of plot you want. Usually this will be the very first one shown.

7. Scroll down to the Xlist and enter the name of the X data list, say L₁.

8. Scroll down to the Ylist and enter the name of the Y data list, say L₂.

9. Scroll down to Mark:  and select what type of marker to use to show the data points.

10. Press 2nd FORMAT to select any display options.

11. You can set the graph size or limits by pressing WINDOW and entering X and Y min and max values or you can press ZOOM and select 9:ZoomStat.  ZoomStat makes the data fill the entire screen by adjusting the graph limits.  If you use the WINDOW option, you will have to press GRAPH to display the plot.

12. If you also want a best fit line drawn, when you do the linear regression enter LinReg(aX+b) L₁,L₂,Y₁.  If the regression has already been done, press VARS, sellect 5:Statistics..., scroll right to EQ, select 1:ReqEQ.  This will enter the regression equation in Y₁.
    (see Plotting a Function (Equation)  and  Linear Regression - fitting a line to data )  
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Linear Regression - fitting a line to data

1. Enter (x,y) data into two lists.

2. Press STAT.  Scroll right to CALC.

3. Select 4:LinReg(ax+b)

4. When LinReg(ax+b) prompt appears on the screen type the name of the x data list, a comma, and then the y data list name.   It should look like the following:   LinReg(ax+b) L₁,L₂. Press ENTER.

5. Two values are calculated. a is the slope and b is the y-intercept.

6. If you want the the regression equation entered as a function enter LinReg(aX+b) L₁,L₂,Y₁.  If you inspect Y₁, you'll see it is now defined as the regression equation.

7. Other regression equations are available.  These include:

   1. LnReg(a+bln(X))

   2. ExpReg(ab^X)

   3. QuadReg(aX²+bX+c)    At least 3 data points are needed.

   4. CubicReg(aX³+bX²+cX+d)        At least 4 data points are needed.

   5. QuartReg(aX⁴+bX³+cX²+dX+e)      At least 5 data points are needed.

   6. PwrReg(aX^b)

   7. Logistic(c/(1+a*e^-bX))

   8. SinReg(a*sin(bX+c)+d)   
      NOTE:  All X values must be equally spaced and calculator in radian mode to use SinReg

   9. NOTE:  A specific regression equation should be used only if you know the data is related by such a model.
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Plotting A Function (Equation)

1. Press MODE.  On the forth row make sure Func is selected (highlighted).   If it isn't highlighted, scroll to it and press ENTER.  Then press 2nd QUIT.

2. Press Y=

3. At the Y₁= line enter the function using x as the variable.  Make sure the = sign is highlighted when done.  If it isn't the graph will not plot.

4. If any Plots are highlighted on the top row turn them off by scrolling to them and pressing ENTER.

5. Press WINDOW.  Enter X and Y min and max values. These adjust what will be seen of the graph on the screen.

6. Press 2nd FORMAT to select any display options

7. Press GRAPH to display plot.

8. NOTE: On the far left of the Y₁= line you'll see a \ mark.  Scroll to this and press ENTER to change it.  This provides options to draw the graph with a thin line, a thick line, shade above the curve, or shade below the curve.

9. NOTE:  If you want function values for several values of X, plot the graph as described above, press TRACE, type in the X values and press ENTER after each one.  The Y (function) values will be printed on the screen.  X values must be between the window parameters Xmin and Xmax.
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Plotting The Inverse Of A Function

1. Enter the function in Y₁ .   EXAMPLE:  Y₁=.5X²-5

2. Press 2nd DRAW and select 8:Draw Inv.

3. At the prompt type Y₁ and press ENTER.   EXAMPLE:   DrawInv  Y₁

4. NOTE:  If you do not want Y₁ plotted make sure the = sign in Y₁= is not highlighted.

5. Alternately just press 2nd DRAW, select 8:Draw Inv, at the prompt enter the function and press ENTER.   EXAMPLE:   DrawInv  .5X²-5
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Plotting A Tangent Line

1. Once a function has been plotted you may have a line draw tangent to any point on the graph.

2. Select 2nd DRAW and select 5:Tangent(

3. Either type in the X coordinate or scroll the cursor to the point where the tangent is to be drawn and press ENTER.

4. The tangent line will be drawn and the equation for the line will be displayed.
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Solving An Equation

1. Press MATH.  Select 0: Solver...

2. Scroll to the top and enter the equation.  Make sure what you enter is equal to zero.  If you are solving  X² + X = 6, enter X² + X - 6.

3. Press ENTER

4. On the screen where you see X=, enter a guess value for X but do not press ENTER.

5. Press ALPHA SOLVE    (SOLVE is over the ENTER key)

6. The new value of X is the solution.

7. EXAMPLE:  Work-Energy Theorem:  (Somewhat involved)
   (1/2)M[V_f² - V_i²] + MG[H_f - H_i] = Fcos(q)S
   A 5kg mass slides from rest down a 3m high ramp a distance of 8m against a frictional force of 2N.  What is the speed of the mass at the bottom of the ramp?

   1. Use Variables V for V_f,  U for V_i,  H for H_f,  Y for H_i

   2. Enter the Solver.. setup as in steps 1 and 2 above and type in the equation:
      .5M(V²-U²)-MG(H-Y)-Fcos(q)S  Then press ENTER.

   3. Scroll to each variable and enter the following but don't press ENTER.
      M=5
      V=1
      U=0
      G=9.8
      H=0
      Y=3
      F=2
      q=180  (make sure calculator is in degree mode)
      S=8

   4. Scroll to V=1 line and press ALPHA SOLVE

   5. V will change to 7.2388 which is the final speed.

   6. Change F to 15 and resolve for V.  Increasing friction decreases final speed.

   7. How could you find the maximum friction that will permit the mass to slide down the incline if it is nudged to start?  Answer:  (Set V=0 and solve for F) 

   8. NOTE:  In this case setting Solver up was tedious, but once it is you can explore a variety of possibilities very efficiently. 
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Zero Of A Function

1. Plot the function. (See Plotting a Function (Equation) )

2. Press 2nd CALC and select 2:zero.

3. Input a value to the left of the zero (Left Bound) by scrolling the blinking cursor on the graph to a point to the left of the zero or use the numeric keys to enter a value.  When done press ENTER. The calculator will prompt for this input.

4. Input a value to the right of the zero (Right Bound) by scrolling the blinking cursor on the graph to a point to the right of the zero or use the numeric keys to enter a value.  When done press ENTER. The calculator will prompt for this input.

5. Input a guess value  by scrolling the blinking cursor on the graph to a point near the zero or use the numeric keys to enter a value.  When done press ENTER. The calculator will prompt for this input.

6. The calculator will then display the zero value.

7. NOTE: There may be other zeros of the function.
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Turn Calculator Into Etch-A-Sketch

1. Press 2nd Draw and select A:Pen

2. Move the cursor with the scroll keys.

3. Pressing ENTER turns printing on and off.

4. When done you can save your masterpiece.  Press  2nd DRAW and scroll right to STO.

5. Select 1:StorePic

6. Enter a number from 1 to 8 and press ENTER.

7. To see your picture later, Press 2nd DRAW and scroll right to STO

8. Select 2:RecallPic.

9. Enter  the number from 1 to 8 used to store the picture and press ENTER.
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Converting Between Rectangular And Polar Coordinates (Useful For Vectors)

1. Rectangular To Polar (Finding Magnitude And Direction of A Vector From Its Components)

   1. Press 2nd ANGLE and select 5:R to Pr(

   2. Enter the X and Y coordinates (or vector components) in the form R to Pr( X,Y) and press ENTER.

   3. The polar radial coordinate (or vector magnitude) will be displayed.

   4. Press 2nd ANGLE and select 5:R to Pq(

   5. Enter the X and Y coordinates (or vector components) in the form R to Pr( X,Y) and press ENTER.

   6. The polar angular coordinate (or vector direction in standard form) will be displayed.

2. Polar To Rectangular (Finding Vector Components From Magnitude And Direction)

   1. Press 2nd ANGLE and select 7:P to Rx(

   2. Enter the  polar coordinates (or vector magnitude and direction) in the form P to Rx( r,q) and press ENTER.

   3. The X coordinate (or vector X component) will be displayed.

   4. Press 2nd ANGLE and select 8:P to Ry(

   5. Enter the polar coordinates (or vector magnitude and direction) in the form P to Ry(r,q) and press ENTER.

   6. The Y coordinate (or vector Y component) will be displayed.
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Minimum Or Maximum Of A Function

1. Plot the function. (See Plotting a Function (Equation) )

2. Press 2nd CALC and select 3:minimum or 4:maximum.

3. Input a value to the left of the zero (Left Bound) by scrolling the blinking cursor on the graph to a point to the left of the max or min or use the numeric keys to enter a value.  When done press ENTER. The calculator will prompt for this input.

4. Input a value to the right of the zero (Right Bound) by scrolling the blinking cursor on the graph to a point to the right of the max or min or use the numeric keys to enter a value.  When done press ENTER. The calculator will prompt for this input.

5. Input a guess value  by scrolling the blinking cursor on the graph to a point near the max or min or use the numeric keys to enter a value.  When done press ENTER. The calculator will prompt for this input.

6. The calculator will then display the minimum or maximum value of the function.

7. NOTE: These values may be only relative min or max values.
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Intersection Of Two Graphs

1. Plot the two functions. (See Plotting a Function (Equation) )

2. Press 2nd CALC and select 5:intersection.

3. Use the scroll keys to place the blinking cursor of the graph to be designated First curve.  The calculator will prompt for this input.

4. Use the scroll keys to place the blinking cursor of the graph to be designated Second curve.  The calculator will prompt for this input.

5. Input a guess value  by scrolling the blinking cursor on the graph to a point near the intersection or use the numeric keys to enter a value.  When done press ENTER. The calculator will prompt for this input.

6. The calculator will then display the x, y coordinates of the intersection

7. NOTE: These there may be more than one intersection.
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Solving A System Of Linear Equations

1. Each equation must be in standard form, such as the systems:
   a₁X + b₁Y + c₁Z = d₁                    5X - 3Y + 4Z = 1
   a₂X + b₂Y + c₂Z = d₂        or         2X  + Z = 2
   a₃X + b₃Y + c₃Z = d₃                    7X -2Y -2Z = -4

   1. The order of the variables X, Y, and Z must be the same in each equation.

   2. Also, the number of equations must equal the number of unknowns.

   3. When using this for a circuit problem, the unknowns will be the currents in different parts of the circuit and the constants will be based on the various resistances and emfs in the circuit.

2. Press MATRIX, scroll right to EDIT and select one of the matrices listed.

3. Enter the number of rows and columns in the matrix.  The number of rows will be the number of equations and the number of columns is the number of constants in each equation.  The matrix for the example above will be a 3x4 matrix, 3 rows and 4 columns.  If a term is missing, it's because the constant is 0.

4. Enter the constants one-by-one in the order they appear in the equations; a₁, b₁, c₁,....  The matrix for the example will be
   5  -3   4    1
   2   0    1   2
   7  -2  -2  -4

5. Press 2nd MATRIX, scroll right to MATH and select B:rref(

6. At the prompt rref(  press 2nd MATRIX and select the matrix you just created.  Type in a closed parenthesis ")" and press ENTER.

7. The calculator will display a new matrix.  The values in the far right column are the values of the unknowns from top to bottom in the order in which they appeared in the equations.  The matrix displayed for the example will be
   1   0   0   .359
   0   1   0   1.974
   0   0   1   1.282
   Thus X = 0.359,  Y = 1.974,  and Z = 1.282.

8. NOTE:  You do not have to have three equations with three unknowns.  There can be any number of unknowns as long as you have the same number of equations.  The matrix you create with the constants will, of course, vary in size with the number of equations.
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Plotting The Derivative Of A Function

1. Press MODE.  On the forth row make sure Func is selected (highlighted).   If it isn't highlighted, scroll to it and press ENTER.  Then press 2nd QUIT.

2. Press Y=

3. At the Y₁= line enter the function using X as the variable.  Make sure the = sign is highlighted when done.  If it isn't the graph will not plot.  If you do not want Y₁ plotted, only the derivative, then the = sign should not be highlighted.  ( The graph shown in the example uses Y₁=2X²-5)

4. Move the cursor to the Y₂= line. If it isn't clear, press CLEAR.

5. Press MATH and select 8:nDeriv(

6. Type in the following exactly as shown...       Y₁,X,X,1)
   NOTE: To enter Y₁ press VARS, scroll right to Y-VARS,  select 1:Functions, select 1:Y₁.

7. If the derivative is of higher order than 1, replace 1 in step 6 by the order of the derivative.

8. If any Plots are highlighted on the top row turn them off by scrolling to them and pressing ENTER.

9. Press WINDOW.  Enter X and Y min and max values. These adjust what will be seen of the graph on the screen.

10. Press 2nd FORMAT to select any display options

11. Press GRAPH to display plots.  
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Area Under A Graph

1. Plot the function. (See Plotting a Function (Equation) )  (The example uses Y₁=2X²-5 with limits -3 and +3)

2. Press 2nd CALC and select 7:Sf(x)dx.

3. The calculator will prompt for the Lower Limit.  This is the Left Bound for the area.  Enter this value by either scrolling the blinking cursor or with the numeric keys.  When done press ENTER.

4. The calculator will prompt for the Upper Limit.  This is the Right Bound for the area.  Enter this value by either scrolling the blinking cursor or with the numeric keys.  When done press ENTER.

5. The calculator will shade in the area and display its numeric value on the screen.

6. NOTE: Area above the x-axis is positive while area below the x-axis is negative.

7. NOTE: This is equivalent to evaluating a definite integral.
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Evaluating A Definite Integral

1. Press Math and select 9:fnInt(

2. Type in the function to be integrated using X as the variable.  Example:    3X²+6.  Type in a coma .

3. Type in X to identify X as the variable to be integrated over. Type in a comma.

4. Type in the numeric value of the lower limit. Type in a comma.

5. Type in the numeric value of the upper limit. Type in a comma.

6. Type in a small number equal to the maximum allowed error in the answer.  Typing 0.0001 means the answer will be rounded off at the forth decimal place.  Type in ).  Press ENTER

7. The calculator will then compute and display the integral.

8. Example:  If f(X) = 3X² + 6 is to be integrated from -1 to 9 then you would enter:
   fnInt(3X²+6,X,-1,9,.0001) ENTER and the calculator will compute 790.000
   NOTE: fnInt( is entered by Pressing MATH and selecting 9:fnInt(.

EXAMPLE: An ellipse with semi-major axis b along the x-axis and semi-minor axis a along the y-axis expressed in polar coordinates is r²=b²cos²q + a²sin²q. Suppose you want to calculate the area of a sector of the ellipse bounded between q₁ and q₂.  If this were a circle you could use A=r²Dq/2, but here you must integrate.  A = integral of ½q(b²cos²q+a²sin²q) with respect to q from q₁ to q₂.     Use a=4, b=6, q₁=p/4, and q₂=3p/4 to define the ellipse and the sector. (Make sure the TI-83 in in radian mode.) Do this integral as described in the steps. The area of the sector is 24.2222. Next find the entire area of the ellipse.  It's 256.6097.
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Math With Lists

1. Type {.1,.2,.3,.4) STO> L₁ and {10,20,30,40} STO> L₂

2. Type L₁ + L₂ STO> L₃; then type L₃ ENTER to view L₃.  See what resulted.

3. Type L₁².  See what results.

4. Plot Y₁ = L₁X²-5  (see Plotting a Function (Equation) .  What do you see?

5. These operations on lists are useful when you have a large number of values in a data set that will each be used in the same calculation.  With lists you only need to enter the operation once.
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Creating A Sequence Of Numbers

1. A list of values calculated by a formula can easily be made.

2. Press 2nd LIST and scroll right to OPS.

3. Select 5:seq(

4. On the screen   seq(   will be printed.  Enter the formula for the values (such as N²+N-1), then the variable name being incremented (in this case N), then the initial value of the variable, the final value, then the increment step from value to value, then  ).  You must separate each entry with a comma.   Press STO> and then a list name (such as L₁) and Press ENTER.  The example would look like:  seq(N² +N-1,N,5,20,2) STO> L₁. 

5. The first, last and increment step values have to be integers.

6. EXAMPLE:  seq(N,N,1,10,1) STO> L₁ creates the list {1,2,3,4,5,6,7,8,9,10}.
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