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gibson:teaching:spring-2018:math445:finaltopics

# Math 445 final exam topics

The final exam will likely have

• 10 problems on matlab (similar to exam 1 questions)
• 5 problems on labs

### 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. 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 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  