ESE 217-Differential Equations & Dynamical Systems

Description

The purpose of this course is to develop the rich and ubiquitous theory of differential equations and, more generally, dynamical systems with strong attention to engineering applications, computer methods, and skills of mathematical inquiry.

The course has (loosely) four sections:

• Weeks 1-3  Basic theory: First-order equations and approximation

• Weeks 4-6  Equilibria and control: Nonlinear DEs, stability, and control theory

• Weeks 7-10  Electro-mechanical systems: Linear DEs and phase space analysis

• Weeks 11-14   Forced oscillation and resonance: Fourier series and Laplace transform methods.

Just like modern engineering, the course will be suffused with computational methods (primarily using Matlab).

Timings

• Lecture: TuTh 4-5:20pm in TBD

• Office hours: Tu 4-5pm, W 11:30-12:30pm in Green 2155.

I'll often offer additional office hours (e.g. around exams) to accommodate schedule conflicts with the regular times.

The AI for this course and their recitation and Piazza office hour times are:

• TBD

  • Recitation: TBD

  • Piazza OH: TBD

Recitations are weekly starting 1/19.

Resources

The main resource for the course is:

• Differential Equations and Boundary Value Problems, Edwards, Penney and Calvis

It's available from the campus bookstore or elsewhere (Chegg, Thriftbooks). We will draw on exercises for homework and will generally follow a similar path through the subject. Note that they recently updated the book - the new version of the fifth edition has 'Tech Update' in the name - but any (even a fairly old) version should be fine. You might be able to find a free online copy, but you didn't hear that from me...

We may also draw on other supplemental resources that will be linked here.

Assessment

This is a mastery-based class, meaning that assessment might feel a bit different to other classes you've taken. The core idea is that mastery gives multiple opportunities to demonstrate understanding, incentivizing making mistakes and reflectively learning from them.

The course has eight learning objectives listed in the spreadsheet above. For each of these, there are three ways of demonstrating mastery:

• IMPL = Implementation: by-hand implementation of a method (once on homework, once on a case study/exam)

• EVAL = Evaluation: rigorous assessment of a method's performance (once on homework, once on a case study/exam)

• CODE = Coding: effective use of computer implementation (once on homework, once on a case study).

There is also an extra objective for participation and contribution to class community, making 8 x 3 + 1 = 25 "checks" in total. These will be converted into a grade at the end of the semester by the rule 1 check = 4% of final grade.

After each piece of assessment is graded you will be given around one week to revise any work that did not meet the threshold for a check to be awarded.

Participation involves being a positive influence in class spaces and recitation, completing regular reflection exercises, and being active on the class Piazza. Each homework contains a praxis prompt where you will practice an additional academic skill; these also count towards participation.

Virtual testing: I will offer a virtual option for synchronous assessment in circumstances such as personal emergencies and quarantine due to sickness or potential exposure to covid-19.

Late submissions: Homework, quizzes and case studies are due at 11:59pm on the day of their deadline. I will accept submissions up to one hour late subject to a 10% penalty where applicable (of your total score; e.g. if you scored 90% this would count as 81%).

Evaluation: Feedback is incredibly important to making this class thrive. Everyone will get a 0.5% grade boost if (on average) 70% of the class responds to evaluations at various points in the semester.

Integrity

• Attempting to cheat in this course is unacceptable and will be strongly penalised. A first offense will be penalised with a zero grade on the relevant piece of assessment. A second offense will be penalised with an immediate fail grade.

• Collaboration is permitted (actually encouraged!) on homework assignments, however each student must write up solutions in their own words.  Please write the names of any other students you have collaborated with at the top of each assignment. Significant similarities between submissions from different students that fail to mention any collaboration counts as an act of cheating and will be penalised as such.

Other Information

• This is a 3 credit class.

• There is no online option for the class except as described above for assessment.

• Prerequisites: ESE 105 (or equivalent)

• Final letter grades will be distributed according to the scale A- 90%, B- 80%, C-70%, D-50%. There are no minuses in the course and pluses will be distributed at discretion of the instructor to recognize outstanding academic engagement and/or contributions to class community.

• Attendance to class or recitation is not required but, as with any advanced STEM class, will usually impact your learning. Notes from class will be posted each week.

• I encourage you to discuss with me, my department chair, or your academic advisor(s) about any concerns you have around classroom dynamics.

• This class will involve a meaningful amount of coding in either Matlab or Python (your choice).

Relevant Policies

• In all academic work, the ideas and contributions of others (including generative artificial intelligence) must be appropriately acknowledged and work that is presented as original must be, in fact, original. You should familiarize yourself with the appropriate academic integrity policies of your academic program(s).

• Except as otherwise expressly authorized by the instructor or the university, students may not record, stream, reproduce, display, publish or further distribute any classroom activities or course materials. This includes lectures, class discussions, advising meetings, office hours, assessments, problems, answers, presentations, slides, screenshots or other materials presented as part of the course.  If a student with a disability wishes to request the use of assistive technology as a reasonable accommodation, the student must first contact the Office of Disability Resources to seek approval. If recording is permitted, unauthorized use or distribution of recordings is also prohibited.  

• WashU supports the right of all enrolled students to an equitable educational opportunity and strives to create an inclusive learning environment. In the event the physical or online environment results in barriers to your inclusion due to a disability, please contact WashU’s Disability Resources (DR) as soon as possible and engage in a process for determining and communicating reasonable accommodations. As soon as possible after receiving an accommodation from DR, send me your WashU Accommodation Letter. Remember that accommodations cannot be applied retroactively.

• If you are a victim of sexual discrimination, harassment or violence, we encourage you to speak with someone as soon as possible. Understand that if you choose to speak to your instructor, they must report your disclosure to their department chair, dean, or the Gender Equity and Title IX Compliance Officer, which may trigger an investigation into the incident. You may also reach out to the Relationship & Sexual Violence Prevention (RSVP) Center to discuss your rights and your options with individuals who are not mandatory reporters -- further resources are available here.

• To ensure that accommodations may be made for students who miss class, assignments, or exams to observe a religious holiday, you must me over email before the end of the third week of class, or as soon as possible if the holiday occurs during the first three weeks of the semester. For more information, please see the university's Religious Holiday Class Absence Policy.

• Before an emergency affects our class, students can take steps to be prepared by downloading the WashU SAFE App.  In addition, each classroom contains a “Quick Guide for Emergencies” near the door.

• WashU provides many resources to support services that address academic, personal, and professional needs.  You can explore resources that might help you here.