18.031 IAP 2016
Haynes Miller and Jeremy Orloff
Course goals
The course will cover linear time invariant systems (LTI). By the end we will have learned about frequency response, impulses and impulse response, the transfer (or system) function, the Laplace transform and systems with feedback. By the end you should be able to do the following things.
- Define the notions of stability, gain, phase lag, frequency response and system function for LTI systems.
- Analyze LTI systems in the frequency domain:
- Compute the transfer function for an 18.03 style constant coefficient linear differential equation.
- Compute the transfer function for a general LTI system from a block; including for diagrams with feedback loops.
- Use the transfer function to determine stability of the system.
- Use the transfer function to find the periodic response to sinusoidal input to the system.
- Interpret the pole diagram of a system in terms of stablity, gain and resonance/
- Define the Laplace transform of a function and compute it for our standard set of functions.
- Use the inverse Laplace transform to compute the unit impulse response of a system modeled by a differential equation.
- Use block diagrams to describe an LTI system.
- Compute the transfer function from an LTI system.
Classes
- Classes: Daily 1:00 - 3:00 pm, from Tuesday January 19 to Friday January 29.
Grading
- The class is pass/fail.
- There will be two problem sets and one (final) exam.
- Problem sets will count for 50% of your grade.
- The final exam will count for 50% of your grade.
- You must turn in both problem sets and the exam to earn a P.
Reading
- There will be reading before each class. The reading will be posted
on the class MITx site.
Problem sets
- There will be two problem sets, due Friday January 22 and Thursday January 28. They must be handed in in class the day they are due. Solutions will be available on the class website the afternoon they are due, so no late homework can be accepted.
- Please be kind to our grader, Alan Wang: Write neatly, and present the
problems in order.
Collaboration
-
We encourage collaboration in this course, we but insist on honesty about it. If you do your homework in a group, be sure it works to your advantage rather than against you. Good grades for homework you have not thought through will translate to poor grades on the exam.
- You must turn in your own writeups of all problems, and, if you do collaborate, you must write on your solution sheet the names of the students you worked with. Failure to do so constitutes plagiarism.
Final examination
- In class on Friday, January 29 at 1 pm
Text
- There will be no text used for the class. We will post the reading to this website.