Course Syllabus

Overview of Topics:

Part 1: Models and Simulation

  • Introduction to Initial Value Problems (IVP), the exponential solution, numerical methods for IVP.
  • Systems of equations, elimination, implicit methods for linear systems of IVP.
  • Nonlinear models, root-finding and Newton's method, implicit methods for nonlinear IVP.

Part 2: Optimization and Control

  • Constrained and unconstrained formulations
  • Classification of minima
  • Iterative methods

Part 3: Uncertainty Quantification

  • Probability: random variable, distribution, moments, conditional probabilities
  • Estimation of the mean and standard deviation, confidence intervals
  • Monte Carlo sampling

Many examples from mechanics (robotics, planetary motion, particle motion, vehicle motion), chemistry, Earth and climate science, biology (epidemiology), etc.

Earth Plane

 

Late Day Policies

  • We offer late days for the submitted component of the problem sets. All students are given 3 late days (24 hour extensions) to use in this course.  Late days are discrete (e.g. a student cannot use 0.314 of a late day). The staff will keep track of late days and feedback for each problem set will include the number of late days the student has remaining. For example, turning a pset on Saturday 7PM when it was due on Friday 5PM would cost two late days. You can use as many of your late days as you want on a pset, but you will be responsible for handing in the following pset on time. 

  • You must ultimately complete every pset, even if you have run out of late days (if you have run out of late days, you will receive a zero but it still must be completed). Failing to do so results in an "incomplete" for the overall course, no matter how well you performed otherwise.

  • To avoid surprises, we suggest that after you submit your pset, you double check to make sure the submission was uploaded correctly. We strongly urge you to see the late days as backup in case of an emergency. Your best strategy is to do the psets early before work starts to pile up.

  • Can I have an extension for the problem set?
    • We grant extensions only in special circumstances where the request comes from S^3.

Collaboration Policies

  • We allow collaborations in groups of no more than three students altogether
    • you are allowed to choose your group for each problem set

  • collaboration does not mean divide and conquer!
    • each student is expected to work on and understand each component of the problem set
    • we will evaluate individual understanding in checkoffs

Checkoff Policies

  • Your total problem set grade = submitted grade + checkoff grade
  • the completion of both components is required for the completion of the course

  • we will send an email with sign up instructions for checkoffs
    • see the course calendar for the tentative checkoffs dates
      • please email course staff if you are unable to make these timeslots
    • please show up on time!
      • we will allow you to reschedule a missed checkoff only if it is your first offense. Subsequent missed appointments result in checkoff grade = 0

  • checkoffs are an important part of the learning experience and are mandatory!
    • late checkoffs will receive checkoff grade = 0.
    • but checkoffs must ultimately be completed, late or not! Failing to do so results in an "incomplete" for the overall course, no matter how well you performed otherwise.
      • You are responsible for ensuring you have completed each checkoff … we will not send email about this.
  • The check-off for a pset submission which you used a late day(s) must still be held on the days offered by the staff.