Topics:

• Introduction to R.
• R help files: Search R functions   R reference card   R help Index
• R files from lectures: beginnings.R   myFirstScript.R   simpleGraph.R   simpleGraph.R   simpleGraph2.R  
  Writing functions, for and while loops:   newtonFor.R   newtonWhile.R  
• Least-square curve fitting to data points Wikipedia Reference
  curveFit.R   beetle.R
• Lecture notes by students: Lecture 1  

Assignment:

1. Online course survey: Please fill out the online survey for our course so we can make it a better one in the future. Thanks. SURVEY LINK

2. Modify the newtonFor.R file above so that newtonForSqrtA = function(A, x, final) computes the square root of A, with a starting value of x, and final number of iterates.

3. Write a function eulerPendulum=function(g, L, x1, x2, h, steps) to compute the solution of the pedulum without friction with g=gravitational constant, L=length, x1=initial position, x2=initial velocity, h=step size, steps=numer of Euler steps. Now, use your function to compute eulerPendulum(1, 1, 0, 1.1, 0.1, 5). Validate your numbers against the ones you obtain from PHASER.

4. Heating of a probe: A student held a temperature probe between her two fingers and recorded the following temperatures every 2 seconds:
   Time     Temp
       00     32.78
       02     33.12
       04     33.37
       06     33.54
       08     33.68
       10     33.78
       12     33.85
       14     33.93
       16     33.98
       18     34.03
       20     34.05
   
   • Plot the temps as a function of time. Is the temp leveling off? Why?
   • Plot the numerical approximation of the derivative from the data vs the temperature. Notice that this graph looks almost linear. Now compute the least squares fit line to this graph and determine the equation of the line.
   • What is the differential equation and the initial condition governing this experiment? Put this differenatial equation into Phaser and plot the solution. Does the Phaser plot resemble the experimental data?