1. What is a transfer function? What is the relation between ODEs and transfer functions? Give an example and show how each representation can be calculated from the other.

2. Which representations of the transfer function can be calculated? 3. What are the poles, the zeros, and the static gain of a transfer function? What are time constants? Give examples and use the calculated poles/zeros to show how different representations of transfer functions relate to each other.

4. What information about the properties of the system do the poles contain? What do the following properties of poles denote with respect to system properties?

1. a real pole with a positive sign

2. a real pole with a negative sign

3. a pole at zero

4. a conjugate complex pair of poles with a negative real part

5. a conjugate complex pair of poles with a positive real part

5. What is the main advantage that transfer functions bring compared to ODEs with respect to mathematical complexity?