The Week of March 15

• Homework: Make a plot of the following two functions
  f(x)=e^-x
  f(x)=1-x+x²/2-x³/6, and
  on the same plot. Bring that plot into a Word document. Add a caption saying "The exponential function and the first few terms of its Taylor expansion." Submit a disk with both Excel and Word files on Monday.

• Monday: Excel demo. Plotting functions.

• Wednesday: More on Excel. Using formulas and plotting.
  Calculating interest. Assuming you have invested $15,000 in a money market account that earnes 3.89% interest compounded yearly, use Excel to calculate the amount of money in this account for the next forty years. Make a plot of the amount versus the year and fit it to an expoential. (Note that your output should have only two decimal places since it represents money.)

  And now for something completely different ....

  The first two Fibonacci numbers are
  F₀=1,
  

  F₁=1,
  and the higher Fibonacci numbers are found using the recursion relation
  F_N = F_N-1 + F_N-2,
  where N=2,3,4,.... So F₂=F₁ + F₀=1+1=2 and F₃=F₂ + F₁=2+1=3, etc.
  Use a formula in Excel to generate the first twenty-five Fibonacci numbers. Make a plot of F_N versus N and fit it to an exponential.

• Friday: More on Excel. Using formulas and plotting. First play with the function RAND(). It gives a random number between 0 and 1. In a cell enter the formula RAND(). Copy the formula down into approximately twenty cells. Take the average and the standard deviation of the numbers. Notice the property that every time you do a calculation using a cell containing rand(), that the cell changes, i.e. you get a new random number. The same thing happens when you copy and paste a cell or cells. That's because you are copying and pasting a formula and the formula gives a random number. To copy the actual numbers instead of the formulas, choose Paste Special and click "values" in the dialog box that arises.

  Now look at the syntax of the IF function
  IF(A1<0.5,1,0)
  The IF function has three arguments, the first is a condition, something that may be true or false, the second argument is the value the function takes on if the condition is true, the third argument is the value the function takes on if the condition is false.

  1. On a new sheet, copy a row of 1's in cells A1 through AZ1.
  2. In A2 enter the formula =A1*IF(RAND()<0.1,0,1) and copy in over to AZ2.
  3. Copy that row down to row 13.
  4. Go to column B1 and sum the numbers in each row.
  5. Plot the numbers in this column and fit them to an exponential.