====== Math 445: exam 2 ======

Exam 2 (Thursday April 7, 2016 10:10-11:00am DeMeritt 240) will cover lecture and labs to date, with emphasis on labs 6 through 9.

You should be familiar with the mathematics and implementation in Matlab code of the following topics

  * [[http://www.ams.org/samplings/feature-column/fcarc-pagerank|hamster dynamics / Google Page Rank]]
  * [[https://en.wikipedia.org/wiki/Newton%27s_method|solving nonlinear equations with Newton's method]]
  * Monte Carlo methods for modeling coin flips and elections
  * 1d, 2d, and 3d graphics

For example, for nonlinear equations and Newton's method, you should understand how to derive the Newton iteration equation $x_{n+1} = x_n - f(x_n)/f'(x_n)$ for improving an approximate solution to the nonlinear equation $f(x) = 0$, and you should be able to write a Matlab function that would implement the Newton method for a given function $f$ and an initial guess $x_0$. 

You should have a good grasp on Matlab syntax we've covered to date. The exam will focus more on recent material:

  * plotting commands: **meshgrid, pcolor, contour, surf, surfc, quiver,** and **colorbar**
  * anonymous functions: how to define and use them
  * random numbers: **rand** and **randn**
  * **for** loops
  
But there will be a few questions on old material as well:

  * vectors and matrices: how to create them, how to access and set their elements, and how to perform mathematical operations with them.
  * the difference between elementwise and linear algebra operations on vectors and matrices.
  * how to set up and solve systems of linear equations using vectors, matrices, and the backslash operator. 
  * the colon operator: how to use it to specify sequences of numbers and access subvectors and submatrices.
  * **fprintf**: how to do basic formatted output with **fprintf**.
  * **function**: how to write your own functions.