====== Math 445: final exam topics ======


===== Matlab basics =====

You should know the basic Matlab functionality for 

  * Arithmetic operations
    * Writing mathematical expressions in Matlab with arithmetic operators ''- + * / ^''
    * Assignment into variables with ''=''.
    * How to enter numbers in scientific notation; e.g. ''3.2e-04'' means $3.2 \times 10^{-4}$.
    * How to enter complex numbers, e.g. ''4 + 5*i''.
  * Logical expressions (which evaluate to true or false)
    * how Matlab represents true with 1 and false with 0
    * comparison operators ''<  >  <=  >=  ==  ~='', e.g. ''3 < 2'' has value false, or 0
    * logical operators ''&& || xor ~'' (and, or, exclusive or, not)
    * how to combine all these to make logical expressions, e.g. ''3 < 2 || 4 > 1'' has value true, or 1
  * Vectors and matrices
    * square bracket notation for creating row vectors, column vectors, matrices
    * when to use commas (separating elements in a row), when to use semicolons (marking end of row)
    * creating vectors with ''linspace'' and colon syntax, e.g. ''x = 0:0.01:4''
    * creating vectors and matrices with ''zeros, rand, randn''
    * matrix-vector multiplication, the definition and meaning
    * ''Ax=b'' problems, forming them from story problems or equations and solving in Matlab with ''\''
    * accessing/setting elements, e.g. ''A(:,3)'' is the 3rd column of ''A''
    * linear algebra operations: ''+ - * \ ^ ' ''
    * elementwise operations: ''- + .* ./ .^''
    * matrix-vector input/output: ''load/save''
  * Plotting functions of one variable 
    * making plots of 1d functions $f(x)$  with ''plot, semilogy, semilogx, loglog''
    * making plots with multiple graphs, colored, dashed, dot-dashed etc. lines, symbol markers
    * annotation: ''xlabel, ylabel, title, grid on, legend, axis, clf, legend, hold on, hold off''
    * graphical data analysis: be able to determine ''y'' as a function of ''x'' from a plot
      * ''plot'' for ''y = mx + b''
      * ''semilogy'' for ''y = c 10^(mx)''
      * ''semilogx'' for ''y = m log x + b''
      * ''loglog'' for ''y = c x^m''
  * Plotting functions of two variables 
    * creating ''X,Y'' matrices with ''meshgrid''
    * plotting functions of two variables with  ''pcolor, contour, contourf, surf, surfc, quiver''
    * changing colors with ''colormap''
    * displaying color scale with ''colorbar''


===== Matlab programming: functions, scripts, loops =====

You should be able to write short Matlab programs to perform specified computations. 
  * how to write a function in a file with ''.m'' extension
  * how to write an anonymous function, e.g. ''f(x) = @(x) x^2 - 3*x + 2''
  * how to write a ''for'' loop to evaluate a sum or product
  * how to write a ''for'' loop to perform a repeated computation

===== Lab material =====

You should have a good grasp of the underlying mathematics and implementation in Matlab code of these labs, i.e. how to ...

  * [[gibson:teaching:spring-2015:math445:lab3]] solve a set of linear equations ''Ax=b'' with Matlab's backslash operator
  * [[gibson:teaching:spring-2015:math445:lab7]] solve a nonlinear equation $f(x) = 0$ by coding ''f'' as an anonymous function and calling Matlab's ''fsolve'' function.
  * [[gibson:teaching:spring-2015:math445:lab8]] determine a transition matrix from a network of links and compute the Google Page Rank.
  * [[gibson:teaching:spring-2015:math445:lab9]] simulate uncertain systems like coin flips and Presidential elections with Monte Carlo simulation.
  * [[gibson:teaching:spring-2015:math445:lab11]], [[gibson:teaching:spring-2015:math445:lab11]], [[gibson:teaching:spring-2015:math445:hw3]] do numerical integration of differential equations with ''ode45''