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gibson:teaching:spring-2018:math445:finaltopics

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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 plot3 contour, contourf, surf, quiver

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