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2 Mathematics MA1S11 (Timoney) 4.2 What a spreadsheet looks like When you start a spreadsheet programme (with nothing saved from before) you should see a grid like the one in the next picture. There are various menu items across the top, various magic shortcut icons around the top an/or side, and the essence of the thing is the grid. The rows of the grid are numbered 1, 2, 3, and so on, while the columns are labels A, B, C, etc. You would normally see a bigger number of rows and columns than what is shown here. The little tabs at the bottom called sheets allow you to have several pages, like in a ledger book, with separate or related stuff on the other sheets. But we will just try to explain what you can do sticking with one sheet. In the picture the top left box, the one in Column A and Row 1, is highlighted (or selected), as indicated by the blackened square around that box, and also you can see A1 written somewhere above. What you can do is put stuff in the different boxes. We call these boxes cells of the spreadsheet and the (main) things you can put in these cells are (i) a number (ii) a word or some words, or any text (iii) a formula

4 Mathematics MA1S11 (Timoney) on the grounds that B6 is in the same position (2 cells left) relative to cell D6 as cell B5 is to cell D Example Suppose we want to calculate the values of y = cos(x) for x = 0, π/10, 2π/10,..., 20π/10 = 2π. (Maybe we want these values for a graph.) In fact for this kind of mathematical graph, spreadsheets are probably not what you should use. But we ll use it now for this anyhow. Let s enter this in the cells A B 1 0 =cos(a1) 2 =A1 + pi()/ (Here the pi() is a way to get at the value π = ) This is what you will see A B Now copy cell A2 and paste it into all the positions A3 to A21. And copy cell B1 and paste that into all the positions B2 to B21. Just to clarify, the effect will be the same as if you had typed all the formulae in the left side of the following, but what you see will be like the right.

5 What is a spreadsheet? 5 A B 1 0 =cos(a1) 2 =A1 + pi()/10 =cos(a2) 3 =A2 + pi()/10 =cos(a3) 4 =A3 + pi()/10 =cos(a4) 5 =A4 + pi()/10 =cos(a5) 6 =A5 + pi()/10 =cos(a6) 7 =A6 + pi()/10 =cos(a7) 8 =A7 + pi()/10 =cos(a8) 9 =A8 + pi()/10 =cos(a9) 10 =A9 + pi()/10 =cos(a10). 21 =A20 + pi()/10 =cos(a21) A B Graphs Graphs (or charts) seem to me to work differently in different programs. With the Google version and the above data, you could highlight cells A1 to B21 and click on the icon for a graph (or find it in the Insert menu). You ll then be presented with various types of graphs or charts to choose from and the option to use column A as labels for one axis. The Google spreadsheet will display π to more than two places by default. If you want ony two displayed, use format on the cell (or click the 123 icon at the top with the cells highlighted). 4.3 Absolute references We may sometimes want to refer to a fixed value, like a tax rate or a VAT rate in a spreadsheet. Or maybe the concentration for some acid, or a PH value. But we might want to allow for that value being changed, and then we want to be able to change our calculations accordingly. We could find a place where we are going to put that value, say cell D2. We could enter 1.23 into that cell for the multiplying factor to add VAT. Now in column A we might list a description of various items we spent money on, in the next column B the cost before VAT of those things, and in column C we might want the cost including VAT. We could enter in cell C1 the formula =B1*1.23 and copy that down column C. That would work, but if we have to change the VAT rate we would have to alter all the formulae. If we put =B1*D2 in cell C1, and copy that to cell C2, it will become =B2*D3, but that is not what we want. We want to get the value in B2 times the value in D2. This can be done by inserting in cell C1 the formula =B1*\$D\$2. The \$D\$2 reference stays as \$D\$2 even after it is copied and pasted. So now if we paste that into cell C2, it will become =B2*\$D\$2, and still refer to the constant 1.23 we have entered in cell D2. Let s say we create this spreadsheet,

6 Mathematics MA1S11 (Timoney) A B C D 1 Item Cost ex VAT Cost inc VAT VAT Rate 2 Door =B2*\$D\$ Lock =B3*\$D\$2 4 Brass handle =B4*\$D\$2 5 Hinges =B5*\$D\$2 6 =B6*\$D\$2 7 =B7*\$D\$2 8 =B8*\$D\$2 9 =B9*\$D\$2 10 TOTAL =sum(b2:b9) =sum(c2:c9) where we are showing what was typed into each cell. However, cells C3 to C9 could be arrived at by copying and pasting from cell C2. It would not save you much, but cell C10 could also be got by copying and pasting from cell C9. The result you would see on the screen would look something like this: A B C D 1 Item Cost ex VAT Cost inc VAT VAT Rate 2 Door Lock Brass handle Hinges TOTAL You might fill in further items and their costs into columns A and B (rows 6 to 9 are still free). As you do that the totals will be updated. Changing the VAT rate entry 1.23 would change the numbers in column C. You might also want to adjust the formatting on the cells B2 to C10 to show 2 decimal places and a perhaps a currency symbol. There are too many tricks you can do to even pretend to tell you about them. 4.4 Further features As mentioned already, spreadsheets can do such a range of things that we can t really hope to convey many of the finer points. About functions that spreadsheets know about. There are really lots, too many to try and explain. Anyhow we don t have the background to understand them all (especially those related to statistics). Here is a small selection

7 What is a spreadsheet? 7 cos(), sin(), exp(),... Lots of mathematical functions. exp(x) means e x. cos(x) is the cos x we use in calculus (with x in radians). sum() Adds up the numerical values in the range. Could be =sum(a1:b10,c3) average() Divides the sum of the numerical values in the range by the number of them. count() Counts how many numerical values there are in the range. So =sum(a1:b10)/count(a1:b10) should be the same as =average(a1:b10) counta() Counts how many not blank entries there are in the range. So a cell with text in it will count. max(), min() Picks the largest (smallest for min) value among those you feed it. if() This allow for complicated things. A simple example is the formula =IF (A2>39,"Pass","Fail") It means if the value if A2 is more than 39, then put the word Pass. If not, put the word Fail. Instead of words, you could have formulae. You could programme a rule that charges 20% tax up to 1500 euro and 40% on anything above like this =IF (A2>1500, 0.2* *(A2-1500), 0.2*A2) Matrix operations Matrix-valued functions seem mysterious to work in some spreadsheet programs but in Google they seem quite easy. For instance the MINVERSE() and MMULT() functions work quite well. You need to feed the MINVERSE() a range of rows and columns that make a square matrix. It produces error codes if the matrix has no inverse. For MMULT() you need to feed it two blocks so that the sizes of the blocks make up matrices that can be multiplied. For instance the formula =mmult(a2:c3,a2:a4) will multiply the 3 2 matrix given by the entries in the block A2 to C3 times the 3 1 block (column) given by the numbers in A2 to A4. The SUMPRODUCT() function can do dot products and there is a TRANSPOSE() to do matrix transposes. Later you may find it useful to know about MDETERM() (which finds determinants). 4.5 Help There are help menus in all spreadsheets I ve seen recently and there are also menus you can put up showing all the available functions (of which there are a few hundred predefined). Richard M. Timoney December 7, 2012

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