Wednesday 2/9/2011 Video of the lecture is available at http://dennett.csi.brandeis.edu/cs177/L7The diary of the lecture and the .m files are attached at the end of this page. Also, here is a link to a latex file in google docs that Brandeisians can edit https://docs.google.com/a/brandeis.edu/document/d/15FMUNqx3j1B2UR4ZXCajsfiTvGng4O6c5fQZSDA_A/edit?hl=en The pdf generated by this is attached at the end of this file. Reading: we are covering material from Chapters 6 and 7 of the Matlab book by Amos Gilat. Learning Objectives for today: students will  be able to write an octave/matlab function computing a mathematical function defined by its Taylor series using both a for loop and with vector operations alone (e.g. hw3)
 understand the time and space tradeoffs for these two ways of writing the function
 be able to explain the different sources of error in Scientific Computing
 be able to plot the relative approximation error for a function they have written (assuming they have an authoritative function to compare it to).
 write simple functions involving for, while, and if statements to compute numberic values
Topics to cover: Taylor series approximations of special functions
 writing exp, sin directly
 writing them without loops!
 modified exponential for any x
 Error in Numerical Computation
 machine error (e.g. Pentium FDIV bug)
 floating point numbers (IEEE754) and roundoff error
 approximation error and eps(x)
 modeling error
 measurement error
 More examples of matlab/octave functions:
 Statistics procedures written from scratch (mean, stdev)
 Matrix multiplication written from scratch
 Useful Matlab functions:
 ind=find(array) returns a list of indices where the array is nonzero
 use this to select subsets of vectors/matrices according to their properties...
