====== Exam 1 topics, Math 445 ======

A few topics that are often points of confusion I've marked with (!). Be sure to study these. 

<code>
  1. mathematical expressions 

    how to write them in Matlab
      - + * / ^   algebraic operations    
      \           solve system of equations Ax=b  (x = A\b)
      =           assignment into variable

    compact scientific notation (e.g. 1.4e-06)
    complex numbers (e.g. 3 + 4*i)
    Inf, NaN (!)

  2. logical expressions (true and false, or 1 and 0)

    (eg x<y is a logical expression, has value 1 or 0)
    <  >  <=  >=  ==  ~=  comparison operators
    && || xor ~           logical operators

    how to combine these to create logical expressions


  3. vectors and matrices
      
      square-bracket notation for creating 
        row vectors
        col vectors
        matrices
        when to use commas and semicolons

      creating vectors with 
        linspace
        colon syntax

      creating vectors and matrices with 
        zeros
        rand
        randn

      matrix-vector multiplication 
        how it works
        dimensional compatibility

      Ax=b problems
        forming them from story problems
        forming them from sets of linear equations
        solving them numerically in Matlab

      accessing/setting elements of vectors and matrices
      (single elements, rows, columns, and subsets (!))
     
      linear algebra operations on vectors and matrices
        + - * \ ^ '
  
      elementwise operations on vectors, matrices (!)
        - + .* ./ .^
 
      matrix-vector input/output
        load, save

   4. plotting     

      making plots 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, hold on, hold off

      graphical data analysis with each of above (!)
        plot:     y = mx + b
        semilogy: y = c 10^(mx)
        semilogx: y = m log x + b
        loglog:   y = c x^m 

   5. functions

      how to write 
        anonymous functions
        named functions in files or at command line 

      evaluating functions on data
      solving nonlinear functions with fsolve

      for loops
        use to compute sums and products
        perform an action repeatedly

   6. miscellaneous built-in matlab functions

      sum
      mean
      size
      save
      load
      class
      who
      fsolve
      prod
      factorial
      fprintf
 </code>