NAME _____________________
Solving Mathematical problems using excel by Prof Robbins
If you have never this spreadsheet there are many excellent references to the fine points about Excel.
Since we will be concentrating on the use of formulas see For example:
http://spreadsheets.about.com/od/excelformulas/ss/formula_begin.htm
Excel formulas have the ability to use most functions you have seen:
Some of the groups of functions you can call upon are
1. Math and trig
2. statistical
3. Logical and database (like if’s etc …CS students take note!)
4. Financial
5. date and time
6. etc
So spreadsheets have proven to very valuable tools in Engineering, Science, Computers etc.
They are used almost as much as mathematical engines like Mathlab!
This is because once you understand a few basic principles it is very easy to set up a problem and
get accurate solutions.
Basics: Open up the Excel program for this discussion
The spread sheet is arranged in columns labeled A,B…etc and Rows 1,2….etc.
Each cell hence has an address..like the first cell is A1 and one can put a number of different
entities in a cell. The cells can be specially formatted to handle the following.
Example important to numerical solving problems.
Numbers to 30 decimal places:
Scientific numbers using the letter E for exponent
Other possibilities exit like Currency, fractions, time, date, accounting..etc.
And of course we can put formulas using numerous functions in the cells.
Essentially formulas use other cells for their numerical content.
Example: (try this to get a sense of how some of the above is done).
Put a 7.5 in cell A1 (IE CLICK THE MOUSE ON THE CELL YOU ARE WORKING WITH)
In cell B1 type +A1
What happened..note that here________________________________
NOTE: THERE IS A LINE ABOVE THE SPREAD SHEET THAT SHOWS YOU WHAT
IS IN EACH CELL YOU CLICK ON! Do you see this!
In cell C1 type +A1/2
What happened..note that here________________________________
In cell D1 type +2*A1 +4
What happened..note that here________________________________
Note how we used a + (sometimes we will enter an = for formulas and functions) to trigger an
operation
Try in E1 putting A1 (ie no + sign)
What happened..note that here________________________________
Try in F1 to put =A1
What happened..note that here________________________________
Relative addressing:
click on B1 and right click choose copy and then go to B2
choose “paste”. Note what formula shows for this cell in the line above the spreadsheet.
What happened..note that here________________________________
This change is called relative addressing..you moved down one cell so the formula which
references A1 now moves down and references A2 which has nothing in it so the answer is 0!
Put a 9 in A2 to see this reference change
What happened..note that here________________________________
When one does not want relative address we can stop movements of the reference by referring to
the cell with $ signs to hold the column or row fixed or both
Examples +$A$1 fixing both
Put the latter +$A$1 in G1 and then copy it to G2 to see how we can fix the number for any cell
avoiding the automatic relative addressing change in the spreadsheet.
What happened..note that here________________________________
Formula practice
Suppose we wish to impement y=ax+b with a=3 and b=8 constants and x going from 0 to 1
in steps of 0.1..in other words a line.
Clear the spreadsheet..highlight all and press delete key.
Cell A1 will be our “a” so put a 3 in it
Cell B1 will be our “b” so put an 8 in it
Column C will contain all our “x’s)
Put a 0 in C1..type the formula +C1+0.1 in C2
What happened..note that here________________________________
Copy cell C2 and paste it in all cells C3 to C11 either individual paste or hightlight all cells and
paste!
Note you should have all values of x we want to consider 0 to 1 in steps of 0.1 in column C
Column D will be all values of y
So in D1 write the formula +$A$1*C1+$B$1 .. we want a and b to be constant and C1 (ie x) to
be a variable. Then copy this formula into D2 to D11
IF YOU MAKE A MISTAKE YOU CAN CORRECT THE CELL INFORMATION BY EITHER
DOUBLE CLICKING THE CELL OR MAKE YOUR CHANGES ON THE LINE ABOVE THE
SPREADSHEET AFTER YOU CLICK THE CELL
What happened..note that here________________________________
NOTE HOW EASY ONE CAN GENERATE ANOTHER LINE BY
Put a 4 in A1 and hit enter or click on a blank cell
What happened..note that here________________________________
Graphing data for 2007 VERSION ONLY for 2003 see below
There are numerous ways to graph our data..in this case we will attempt to graph the line you just
Generated
1. highlight all values in D
2. go to the “insert” column and pick chart
3. select “line”
4. pick first line graph 2D version
5. You should see the y values on a graph with the x values only being the point number
6. To have our true x values portrayed on the x axis do the following
7. Click on the numbers 1 to 11 on the x axis this highlight them
8. Right click and select “select Data”
9. A box of select data source pops up
10. The box is subdivided, click on edit in the HORIZONTAL CATERGORY
11. Only ie the x axis
12. Select the c column values
13. Click ok on the box that appears
14.Again click ok on the large Select data source box
Looking over your graph now describe what happened?\
Can you move the embedded graph around the spreadsheet?_____________________
There are numerous other embellishments to be put on a graph
PRINT THE SPREADSHEET (DO A PREVIEW FIRST) AND HAND IN WITH THIS
EXERCISE!
(Graphing data for 2003 VERSION ONLY
There are numerous ways to graph our data..in this case we will attempt to graph the line you just
Generated.
15. go to the “insert” column and pick chart
16. select “line”
17. pick “next”
18. select “column”
5 click the spreadsheet symbol and then highlight the column D1 to D11 then hit enter
You should see the y values on a graph with the x values only being the point number
To have our x values portrayed
Click the series tab at the top and note at the bottom “Category x axis labels”
Click the spreadsheet symbol on this area and highlight all the C column values and pick enter.
Then click finish!
Note the graph!
What happened..note that here________________________________
Can you move the embedded graph around the spreadsheet?_____________________
There are numerous other embellishments to be put on a graph
PRINT THE SPREADSHEET (DO A PREVIEW FIRST) AND HAND IN WITH THIS
EXERCISE! End of 2003 version only)
Solving problems
In general it is best to organize your approach. I recommend the following steps not
necessarily in this order.
1. what are the constants and known variables
2. what are you looking for; Unknowns?
3. What laws or formulas must you use.
4. Solve(set It up) the formula(s) for the unknown in terms of what is known
5. plug in the numbers in the formula ..calculate
Example: What is the frequency of the red color 600nm?
Assume Formula c is what you know
then 1. constant c=speed of light=3.0 x 108 m/s and we know the wavelength
nm=600x 10-9 m
2. we are looking for the frequency 
3. Formula solution
c3.0 x 108 m/s / 600x 10-9 m = 5.0 x 1014 /s or 5.0 x 1014 cps
Note in a paper solution we carry the units to be sure our final unit is correct!
Spread sheet solution. Generalized to many wavelengths.
Set up a new spread sheet (select the Symbol for New blank document is a blank page)

Click on A1 right click Format cells and note the tabs and pick the Number tab and the many
choices some of them were mentioned above.
Select the scientific choice with 2 decimal places and then click OK!
TYPE 3.00E8 then enter in cell A1
What happened..note that here________________________________
This is our speed of light constant for the problem
Format B1 and C1 like you did A1
In B1 enter the wavelength as 600E-9
What happened..note that here________________________________
In C1 we enter an equivalent to the formula c
Or we want c1 to have the constant in A1 or $A$1 divided by the value in B1 which we can
change so enter the formula +$A$1/B1 in C1
Did you get the same answer as above.
What happened..note that here________________________________
Since we are referencing column B for our wavelengths we can use the relative addressing to do
more of the same so format cells B2 to B5 scientifically and enter the wavelengths,
400nm,550nm,678nm and 10.17nm. as you did for the 600nm
Copy the formula in C1 to C2 to C5.
What happened..note that here________________________________
Print the spread sheet
TASKS: Do these on one spread sheet and PRINT!
1. SET UP FORMULA 2.2(YOUR TEXT) ON THE SPREAD SHEET AND SOLVE FOR THE
TWO SOLUTION GIVEN AFTER FORMULA 2.3
NAMELY 2.2 b1/b2 =10(m2-m1) m1 = 1 m2 =6 and the other m1 = 6 m2 =26
TO DO THIS USE INSERT THE “POWER” FUNCTION IN A CELL TO GET 10 TO A
POWER (m2-m1) . WHEN YOU PICK A FUNCTION EXCELL GIVES YOU DETAILS ON
HOW TO USE IT..
Did you get the correct answers? (102 and 108). No ? see me
2 SET UP FORMULA 2.3 m2 – m1 =2.5 log10(b1/b2) AND SOLVE FOR m = m2 – m1 for a
factor of 106 in brightness.
TO DO THIS INSERT FUNCTION “LOG10”
Did you get the correct answers? (15 mag). No ? see me
2. DO PROBLEMS 2.1, 2.2 AND 2.3 ON THE SPREADSHEET!
PRINT ALL