Some pointers before starting the course:

I made the syllabus by looking at various past syllabus for courses taught in the department.
I was coordinating all three sections: one in-person section and two asynchronous online section.
I was teaching the in-person section and there was an instructor for the online sections.
I wanted to make the grading policy as similar as possible for all sections.
I chose to have a video assignment for all sections. This will definitely encourage students who are falling behind to keep up with the online course, and at the same time, I felt that this would be useful to have the in-person students to watch external resources outside of class. Steve Brunton’s excellent videos on differntial equations influenced me towards this direction.
There is a 5% grade for attendance/participation in the in-person course. I gave the online instructor his discretion to assigning this 5% in anyway he likes for the online course.
I decided to not to have a MATLAB/Mathematica coding component. This is mainly because the online students are mostly outside campus and they do not have access to the math softwares available on campus. Of course they could access the servers here, but it will be difficult to make everyone in the online classes follow the procedure for accessing the server. I would reconsider this if there were more students in the in-person section. But, I would definitely have a coding component if this was a Spring or Fall semester.
I showed my syllabus to my supervisor and several colleagues for their opinion on it, and asked for suggestions.

Course Schedule

Since this is a 8 week course, I had to skip some sections from the usual topics taught in spring and fall semesters.
My goal was to emphasize the basics and leave ample time to discuss phase diagrams.
All students except one were engineers. One student was a math major. So I decided to emphasize engineering and mathematical applications.
Considering my goal to teach them phase diagrams, I had to also take into account the fact that Linear Algebra is not a prerequisite for this course. So I need to teach basic linear algebra within a few days.

Grading

From my experience, students usually perform poorly on average on the finals. So, I wanted to put less weights on the exams than the homework considering the difficulty of the course and the short length as a summer version. This was the best distribution I could come up with so as to keep the weight for the final small but at the same time more than the weight for each midterm. I should note that this is only disadvantegous for the rare student who performs badly on the midterms, but manages to do extremely well on the final.

Exam

3 exams and 1 final is highly recommended and almost every course follows this pattern.
For the in-person section, I wanted to have their exams in class. I did have the option to do it online, but I did not like that option for many reasons. In person exams are the best way to test their understanding of the material while avoidinf cheating possibilities.
For the online sections, I had no choice but to have their exams online. I decided to have a zoom room open for them to keep their cameras on. I also required them to have their camera pointed towards their writing desk. This could be their phone for instance.
There are online proctoring softwares available, but the department does not use those.
There are strict instructions of online exam. They have to have their cameras on at all times. I will be proctoring the exam and record the zoom call. If any student does not have their camera on, I ask them to turn it on. If no response after several attempts, I will message and email them. After several attempts if they do not respond at all, I will seek an explanation from them. If I suspect of cheating instances, I will dock their grade.
All these warnings about the procedures will be provided before hand.
All the repurcussions for not cooperating should be made clear in the beginning of the course.
It is pretty common these days to allow students to have a sheet of notes during the exam with whatever formulas, notes they prefer to write. I decided to allow this for exams.

Online Exam specific

They were giving two timeslots for selection. One was morning and the other was evening. This was in consideration for their working hours and other responsiblities.
Not everybody could make it. The students who could not make it during these times, were given different exam appointments according to their schedule.
There are many online proctoring options, but most of them are paid services.
I didn’t have a choice for online options, and since the class wasn’t too big, I chose to have the exam on zoom.
I gave clear instructions on how to setup their devices for zoom. Their device camera would record their desk, their faces, and their laptops from the side.
All students followed the instructions.

Exam 1 learning from experience

There were 7 questions for the 75 minutes exam.
I noticed that there were very few students who finished the exam early in both the in-person and online exam.
I realized that in future exams, either I should shorten the number of questions, or the length of one of the questions. Otherwise, 7 questions is not too bad for the exam.
The exam was similar to the homework and practice problems.

Homework

Written homework is better than online homework for many reasons. Incorporating both might be a good option.
Written homework will show the student’s complete work.
Online homework requirements mainly require the student to enter the final answer.
We have to emphasize many times in many courses that the student needs to show their work.
Math should be written on paper to make sense.

Homework 1 learning from experience.

Homework 1 was too long ~ 18 problems, especially for online students because they were also assigned quite a few video assignments, and quizzes by the online instructor.
Learning from this, the next homework was made shorter ~ 12 questions.

Video Assignments

Video assignments were assigned to both the in-person and online classes, although they were different assignments.
The online students had to watch the instructor’s videos on the topics, while, the in-person students had to watch the beautiful videos of Steve Brunton and 3Blue1Brown.

Student Group Work during class

This is an amazing pedagogical technique that should be applied to every small to medium sized class.
Humans learn math by solving problems, hard or easy. Also, we don’t learn math in a linear fashion. Some topics are learnt only in a bigger context. With the right motivation and presentation of topic, math can be made cooler.
Lecturing for 75 minutes is not recommended.
I lecture at most for 35 minutes. Every day, the students were divided into groups and they worked on problems. Most problems were non-trivial, because it makes them think and discuss ideas with their peers. Just plug and chug problems won’t make them learn.
There were very few word problems on exams, but class problem solving sesssions did cover quite a few word problems.