gibson:teaching:spring-2018:math445:finaltopics

**This is an old revision of the document!**

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

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. 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
`plot3 contour, contourf, surf, quiver`

7. hamster dynamics / Google Page rank

- derive a transition matrix from a network of links
- write code to iterate

8. nonlinear equations

- know Newton iteration equation
- derive Newton iteration equation graphically or from Taylor series
- write function that uses Newton iteration to find solution of for given function and initial guess

8. differential equations: given a system of differential equations for vector , write

- code for the function which computes
- code that integrates numerically using ode45
- code that plots the solution of the numerical integration
- code that draws quiver pliot for vector field

gibson/teaching/spring-2018/math445/finaltopics.1525371110.txt.gz · Last modified: 2018/05/03 11:11 by gibson