Difference Equations Skill List

Difference Equations

+ DE01: Understand notation and be able to write out equations for simple difference equations

Be comfortable using subscripts and understanding what we mean when we write $X_{n} = 2 \times X_{n-1}$ and be able to work out the value of, say, $X_{4}$ given $X_{0}$ and an expression for $X_{n}$.

+ DE02: Translate a problem into difference equations

Recognize in a problem what the quantities of interest are, what the time periods are, and what amounts and rates represent the differences from one period to the next.

+ DE03: Create and use Pn+1 vs. Pn charts to assess difference equation system behavior

1. Constructing difference equation chart from equations/table with 45 degree line
2. Be able to explain how chart is made and what a point (x,y) on the line means, explain what 45 degree line represents
3. Based on slope of DE line, describe kinds of equilibria, if any
4. Describe difference equation in $Pn+1 = a Pn + b$ terms and caclulate Pe from this.

+ DE04: Implement difference equations model in Excel and graphically display outcome

1. Translate standard subscript notation into Excel formulas
2. Use autofill to extend integer time periods and formula for quantity of interest
3. Use other cells to contain parameters that are referred to in the difference equation formula
4. Make appropriate use of relative and absolute cell references so that formulas autofill correctly
5. Use a "spinner" to make a parameter variable; use a "divide by (a power of) ten" formula to make a spinner control parameters of arbitrary precision.
6. Format text in Excel to show subscripts.
7. Create XY scatterplot charts with legends and titles depending on data

+ DE05: Convey understanding of relationship between difference equations and related models/techniques.

Describe how to get from difference equations to stock and flow models

+ DE06: Suggest indications and contraindications, identify and respond to typical concerns and caveats

1. Describe assumptions and caveats