Table of Contents

Math 445 final exam topics
- - Matlab topics
  - Labs

Math 445 final exam topics

The final exam will likely have

10 problems on matlab (similar to exam 1 questions)
5 problems on labs
2 essay questions about your experience with labs and lecture

Matlab topics

1. creating and manipulating vectors and matrices

colon operator: creating vectors of integers, over a range and with a given increment
accessing elements of vectors
accessing rows, cols, and elements of matrices
determining the size of vectors and matrices
dot syntax for elementwise operations versus linear algebra operations

2. linear algebra

matrix-vector multiplication
- mathematical definition
- computing numerical examples on pencil and paper
- computing numerical examples in matlab
converting story problems to Ax=b problems
solving Ax=b problems in Matlab

3. evaluating complex mathematical expressions in Matlab

e.g. $\sum_{n=1}^{11} x^n/n!$ with sum

4. xy plots

creating 1d grid with linspace (or logspace)
evaluating expressions over 1d grids using dot syntax
plot command: plot y versus x, specify colors and line styles
labeling axes, titles, grid, legend
semilogy, semilogx, loglog
1. what kind of functional relationships each is appropriate for
2. estimating functional relationships from graphs of each

5. writing simple functions in Matlab

syntax for function in a file
syntax for anonymous function
functions involving for loops (e.g. matrix-vector mult)

6. 3d graphics

creating 2d grids of coordinates with meshgrid
evaluating functions on 2d grid with dot syntax
Matlab functions contour, contourf, surf, quiver and plot3

Labs

7. hamster dynamics / Google Page rank

derive a transition matrix $x^{n+1} = A x^n$ from a network of links
write code to iterate $x^{n+1} = A x^n$

8. nonlinear equations $f(x) = 0$

know Newton iteration equation $x_{n+1} = x_n - f(x_n)/f'(x_n)$
derive Newton iteration equation graphically or from Taylor series
write function that uses Newton iteration to find solution of $f(x) = 0$ for given function $f$ and initial guess $x_0$

8. differential equations: given a system of differential equations $dx/dt = f(x)$ for vector $x$ , write

code for the function $f$ which computes $dx/dt = f(x)$
code that integrates $dx/dt = f(x)$ numerically using ode45
code that plots the solution of the numerical integration
code that draws quiver pliot for vector field $dx/dt$