BME 315 – Homework 1
Due Sunday, January 25, 2026 11:59p
20 points
1) (4 points) Give 2 examples of heuristics that you use daily.
2) (4 points) In the gastrointestinal system, we can define and study many subsystems in terms of
the input and output. What are the inputs and outputs for the stomach?
3) (4 points) Given the following systems:
a) 4
b)
c)
𝑑𝑦
𝑑𝑡
𝑑4 𝑦
𝑑𝑡 4
𝑑2 𝑦
𝑑𝑡 2
𝑑𝑥
+ 𝑦 + 4 = 𝑑𝑡 + 5𝑥
𝑑𝑦
+ 𝑎(𝑡) 𝑑𝑡 = 𝐹(𝑡)
𝑑𝑥
𝑑𝑦 3
4
+ 2 𝑑𝑡 + ( 𝑑𝑡 ) + 𝑥 = 𝐴 + 𝐵𝑐𝑜𝑠(𝑡)
3.1) Classify the systems as linear or non-linear
3.2) Identify the order of the systems for each equation
4) (4 points) Place the following terms into the following 3 categories:
a) not mathematically definable
b) definable but dimensionless
c) definable with dimension
Give dimensions for dimensional quantities.
- Absolute zero
- Avogadro’s number
- Barometric pressure
- Cardiac output
- Clearance
- “Counts per minute” as a measure of a radioactive isotope
𝑑𝑁
- − 𝑑𝑡 , N = number of bacteria and t = time
- Neonatal period
- Molarity
- pH
- R, constant of ideal gas
- Senility
- Stroke Volume
- Turbulence
- White blood cell count
- Zygote
5) (4 points) A pressure transducer is calibrated using a column of H2O with the following readings:
Pressure [cm H2O]
Output [V]
50
1
100
1.4
150
1.8
200
2.2
What is the calibration relation? Write the sensitivity and offset with units. What is the pressure if
the output is 0.75 V?