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 2:30-3:50pm in Rudolph 203

• 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 two AIs for this course and their recitation and Piazza office hour times are:

• Wensi Li

  • Recitation: W 4-5pm, McKelvey 1030

  • Piazza OH: W 7-8pm

• Praneel Panchigar

  • Recitation: F 12-1pm, Green 1117

  • Piazza OH: Th 4-5pm

Recitations are weekly starting 1/22.

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

There are four types of work to be submitted during the course:

• Homework: ~biweekly homework sets submitted through Gradescope (including a component using Matlab).

• Mastery quizzes: ~biweekly quizzes alternating between virtual and in-person.

• Reflections: ~monthly reflections on your experience and growth through the semester.

• Case studies: two case studies due 3/24 and 4/28.

Grade

• Participation (20%)

• Case studies (40%)

• Mastery (40%)

Participation: This includes active engagement in class, homework completion, and monthly self-reflections. I will allow for one missed homework and one missed reflection without impacting your grade. After this point each missed homework or reflection counts as -1% of your grade.

Mastery: This course uses mastery-based grading. This is designed to provide a lower pressure environment where developing specific skills in the course is prioritised as opposed to assessing whether you can successfully take tests. This part of the grade involves completing mastery objectives throughout the course. There are 11 objectives found in the Objectives tab of the spreadsheet below.

To demonstrate mastery for an objective you need to do three things:

1. provide a complete solution to a question on that topic during a quiz

2. provide a complete solution to a nominated question on that topic as part of homework

3. provide a Matlab demo showing your ability to analyse examples around that topic.

Quizzes and homeworks are ~biweekly; you can submit a Matlab demo for each topic at any time during the course. Objectives will appear multiple times on quizzes and homework (listed in the spreadsheet below under Objectives).

There is no obligation to complete all questions on a quiz (e.g. if you already have a quiz check for an objective there's no need to attempt it again). Indeed, you shouldn't expect to have time to complete all questions so you will need to be strategic about which objectives you want to attempt.

Here is a mastery cheat sheet to help keep track of which objectives you've achieved.

At the end of the semester we'll translate mastery checks into a grade via the formula 1 check = 3% for the mastery portion (40% of the total grade). I'll give you 1% for free :-)

Virtual testing: I will offer a virtual option for quizzes 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 (of your total score; e.g. if you scored 90% this would count as 81%).

Makeups: Because of the features above I don't allow for makeups under any circumstances.

Homework: Each homework contains a "praxis" prompt where you will practice an academic skill: communication (via recording a video solution to one problem), collaboration (partnering with someone else to complete a problem and providing feedback), education (preparing a mock lesson plan to explain a concept).

Evaluations: 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.