Math 445: final exam topics

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 .
  • 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 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

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

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

• lab3 solve a set of linear equations Ax=b with Matlab's backslash operator
• lab7 solve a nonlinear equation by coding f as an anonymous function and calling Matlab's fsolve function.
• lab8 determine a transition matrix from a network of links and compute the Google Page Rank.
• lab9 simulate uncertain systems like coin flips and Presidential elections with Monte Carlo simulation.
• lab11, lab11, hw3 do numerical integration of differential equations with ode45