Math 445 final exam topics
The final exam will likely have
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
converting story problems to Ax=b problems
solving Ax=b problems in Matlab
3. evaluating complex mathematical expressions in Matlab
e.g.
![Math $\sum_{n=1}^{11} x^n/n!$](/dokuwiki/lib/exe/fetch.php?media=wiki:latex:/img86be1c9d4645eee02d61fd82b69caa7c.png)
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
what kind of functional relationships each is appropriate for
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
![Math $x^{n+1} = A x^n$](/dokuwiki/lib/exe/fetch.php?media=wiki:latex:/imgb13ab5bff59dd83eb8d96de4dd4f671d.png)
from a network of links
write code to iterate
![Math $x^{n+1} = A x^n$](/dokuwiki/lib/exe/fetch.php?media=wiki:latex:/imgb13ab5bff59dd83eb8d96de4dd4f671d.png)
8. nonlinear equations
8. differential equations: given a system of differential equations
for vector
, write