I don't know the expansion of K3 and K4 in RK4.
The below is taylor of RK4
.
where free fall equation given by:
.
Definition RK4 of free fall equation:
where k1 is
and k2 is
and k3 is
and k4...
I don't know the expansion formula of K3 and K4.
Please tell me about how to expand.
Related
Tried different approaches, but the best I could came with is:
=IF($C$2:$C$65365=B4, COUNTA($G$2:$G$65365))
but it returns #SPILL
B
C
D
E
F
G
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Use COUNTIFS()
• Formula used in cell D7
=COUNTIFS(C2:C5,C7,G2:G5,"<>")
Using SUMPRODUCT()
• Formula used in cell E7
=SUMPRODUCT(--(C2:C5=C7)*(G2:G5<>""))
Using some fancy functions to simplify, clarify and improved performance. LET()
• Formula used in cell F7
=LET(criteria_range1,C2:C5,criteria1,C7,
criteria_range2,G2:G5,criteria2,"<>",
COUNTIFS(criteria_range1,criteria1,criteria_range2,criteria2))
I have 4 equations, with 4 unknowns, a,b,c,e
w = c + 0.43*a
x + gb = pc + 2*e
y + 2a + hb = qc + 20.43a + e
z + bi = cr
What would be the best way to solve this in Excel?
I searched and found that LINEST might be a good function to use, but couldn't get it to work
Thanks
First rewrite all you formulas in the form
Ai*(a)+Bi*(b)+Ci*(c)+Ei*(e)=Ki
Then for each equation fill out a row in the matrix
A1 B1 C1 E1 a K1
A2 B2 C2 E2 x b = K2
A3 B3 C3 E3 c K3
A4 B4 C4 E4 e K4
Then use MInverse and MMultiply functions to solve for a,b,c and e
A,B,C,E are the constants multiplying each variable. Set them to 0 when they are not in the formula, and make sure you carry the negative sign.
i is just a way to represent the equation number.
K is the constant in the equation with out a variable attached to it.
So provided I did the formula rearrangement properly, one possible result would be:
Cant take it farther than this as numbers would be needed for g, p, h, q, i, and r (not to mention w, x, y, and z). Though you could set those up in cells so you sheet would automatically update when you entered values.
I have an equation that I am trying to format in Excel:
Sigma (from 1 to n) where n=10 of (xi-xo)^2
I have 10 values for xi and xo=0.5 for this particular problem. How would I go about summing this?
Use SUMPRODUCT:
=SUMPRODUCT((A1:A10-B1)^2)
Where A1:A10 holds the 10 numbers xi and B1 holds xo
So the blue line graph has values from column CM (x values are in column CF, sorry for the confusing presentation). I want to recreate the polynomial trendline that I had excel generate for it, which is what I'm trying to do in column CH, as you can see from the formula bar.
Excel gives me the formula y = -0,0006x^2 + 0,013x + 0,1878 (shown on the chart) which I then have entered into the values in column CH.
The result is unfortunately not even close (displayed as the orange line graph). Is there any person here sharp enough on maths to tell me what I'm doing wrong?
This is the formula to obtain 2nd Order Polynomial Trendline:
y = (c2 * x^2) + (c1 * x) + b
c2: =INDEX(LINEST(y,x^{1,2}),1)
c1: =INDEX(LINEST(y,x^{1,2}),1,2)
b: =INDEX(LINEST(y,x^{1,2}),1,3)
So now, just examined your formula, you have incorrect parameters (b, c1 and c2) used so the result is different.
Here are the formulas I used to obtain these three parameters:
c2: =INDEX(LINEST($CM$1234:$CM$1262,$CF$1234:$CF$1262^{1,2}),1)
c1: =INDEX(LINEST($CM$1234:$CM$1262,$CF$1234:$CF$1262^{1,2}),1,2)
b: =INDEX(LINEST($CM$1234:$CM$1262,$CF$1234:$CF$1262^{1,2}),1,3)
Then I got:
c2 (cell CG1227) = -0.05675
c1 (cell CG1228) = -0.04025
b (cell CG1229) = 0.25509
Now, from cell CH1234, this formula is used:
=($CG$1227*CF1234^2)+($CG$1228*CF1234)+$CG$1229
I have the outcome matched with the Polynomial Trendline. Try and see if this works for you.
When we add a trendline to a chart, Excel provides an option to display the trendline equation in the chart.
We can then use these formulas to calculate predicted y values for give values of x
The formulea are nicely listed by SpreadSheetPage.Com
I wanted to implement the same in the excel sheet for a dataset like given below:
Year Value
1990 400
1991 494
1992 449
1993 554
1994 600
1995 499
1996
1997
1998
1999
2000
As you can see, I wanted to project the values for the years 1996 to 2000 using 2nd Order Polynomial.
Using the equations provided by SpreadSheetPage.Com
2nd Order Polynomial Trendline
Equation: y = (c2 * x^2) + (c1 * x ^1) + b
c2: =INDEX(LINEST(y,x^{1,2}),1)
C1: =INDEX(LINEST(y,x^{1,2}),1,2)
b = =INDEX(LINEST(y,x^{1,2}),1,3)
I calculated C2 and the stored the value in a cell whith cell address say C2.
Similarly, I calculated C1 and stored the value in a cell with cell address say C1. I also calculated b and stored the value in a cell with cell address say C3.
Then, in the cell besides the year 1996 (whoes value I want to project), I entered the formulea = (c2 * x^2) + (c1 * x ^1) + C3 and Ctr+Shift+Entered for the array formulea while selected the value cells from 1996-2000.
The results were not as expected. I am sure I am not using these equations in their proper way. Any help in this regard will be highly appreciated.
Please not I have made named arrays x and y for known x's and known y's respectively.
Given the limitation that you don't provide your actual or expected results:
Assume your known table is A1:B7, and your ranges are named as you mentioned:
B8: = (C$2 * A8^2) + (C$1 * A8 ^1) + C$3
and fill down to B12
Using a different function, you could use:
B8: =TREND(y,x^{1,2},A8:A12^{1,2})
Then select B8:B12 and enter as an array with ctrl+shift+enter. Note that this function may be inaccurate in versions of Excel prior to 2007.
EDIT
Note that the original formula can be entered as an array if we replace A8 with A8:A12; and the TREND function can be entered normally, and filled down, if new_x is entered as a single cell, instead of a range.