Basic Maths Foundation Flashcards
How does Vensim work?
- simulation tool
- working mechanisms
- —> mathematics : integration & differentiation
discrete time:
—-> time step ≠
continuous
General steps for level determination:
- Calc new rates
- Updates levels after short period of flow
- Repeat
What is the net flow rate?
Net flow rate = inflow rates - outflow rates
What is the level formula?
GRAPH EXAMPLE:
A bathtub filling up with water at 0.5L/min. The tub originally had 1.0L of water. There is no water flowing out.
- rate = constant
- rate graph:
water after 1 min:
water after 2 min:
water after 3 min:
A bathtub filling up with water at 0.5L/min. The tub originally had 1.0L of water. There is no water flowing out.
What is the level graph?
rate ≠ constant then:
Visual integration: (3)
- area under curve (rate curve)
- sum of many small things - needed if rate changes
- Riemann sum
What is the formula for the level?
Calculating the Riemann sum graphically: (4) ≠ 100% accurate
- Slice curve = equal rectangles to horizontal
- Use L/R point on horizontal = approximate height of the rectangle
- Calculate rectangle areas
- Sum areas
Is the error large or small?
- 4 calculations
- width = t
- t = large
- 8 calculations
- t = smaller
- more calculations
- trade off between accuracy + computing power
integral is the ____ of a derivative.
reverse
Derivatives:
What does the slope represent?
Integration: integral = level
y(t) =
y(a + m△t) =
y =
y(n△ t) =
