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Website for M303 and MAT704: Differential Equations,

Fall 2026

This the website for the course M303 and MAT704:Differential Equations.

I will be maintaining this website regularly during the course; please visit it regulalry.

This is a course in Ordinary Differential Equations. You are expected to have a good knowledge of basic Real Analysis.

This course is an important prerequisite for many other topics, the most obvious one being Partial Differential Equations. The course is also important if you wish to have a good understanting of smooth manifolds (for example, when one needs to show existence of integral curves for a vector field). The course is also very useful if you wish to study dynamical systems.

We will be using the following references

1) ``Ordinary Differential Equations'' by Nandakumaran, Patti and George.

2) ``Differential Equations, Dynamical Systems and an Introduction to Chaos'' by Hirsch, Smale and Devaney.

We might use other references from time to time.

3) ``Chaos: From Simple Models to Complex Systems'' by

Cencini, Cecconi and Vupliani. Although this is a physics book, it is quite interesting and we might consult it from time to time (albeit from a more mathematical and rigorous point of view).

Grading: Continuous Assesment (Homework + Quizzes) = 30%

Mid Term = 30%

Final Exam = 40%

Grading will be absolute.

Attendance is compulsory. I will deduct two points from the Continuous Assement portion for every single class that you miss without a valid reason. Hence, even missing one class can affect your grade (for example, if your final score was otherwise 91, but you missed one class, you will end up getting an AB instead of an AA).

Attendance will be taken 10 minutes after the class starts. If you enter the class after 10 minutes, you will be marked absent.

Examples of valid reasons include: being unwell accompanied with a doctor's note, an important exam that you might have to give (such as CSIR etc) that clashes with the timing of the course or a family emergency. These reasons have to be accompanied by a valid proof (for example, if you are claiming that you missed a class due to an exam, you will need to show me your admit card for the exam). Examples of reasons that are not valid include: caliming that you are unwell without any doctor's note, saying that you woke up late etc. If you have a valid reason to miss a class, I will not deduct the two points. However, you are still responsilbe for studying the topics that you missed.

If your attendance is below 80 percent, you will not be allowed to sit for the final exam. I will however, mark everyone present for the FIRST week of classes. You are nevertheless responsible for all the material covered in the first week.

If there is a foreseeable reason for which you MIGHT need to miss a class, you should inform me as soon as possible and see if I will give permission (namely if I will deduct the two points or not). For example, if you need to attend an academic conference and need to miss classes because of that, you need to see if I will give permission. DO NOT make plans first and then inform me at the last minute that you are going to miss classes; that way you might be disappointed. Make your plans AFTER speaking to me. My remarks DO NOT apply to situations that are beyond your control (such as a sudden emergency) for which you need to leave on a short notice.

Clarification: The continuous assessment portion will be computed as follows.

Let T1 be the sum total of the scores you get in the HW and quizzes. Let

E1 be the marks I award you for attending the extra classes I take (how much is

E1 will be decided by me later on). Let N be the number of (regular) classes you miss

without a valid reason. Let T2:= Min(30, T1+E1). Let T3 = T2-2*N. Finally

let T4:= Max(T3, 0). Your continuous assesment score is T4.

My opinion on using AI is as follows. If used effectively, it is fantastic. If it used in the wrong way (which is probably how most people use it), it can be a disaster. It is like fire. AI is NOT to be used at the last moment to solve your homework problems. A short but nice video on how to use AI effectively is here. In short, I encourage you to use AI (but this is my personal view and I admit I may change my opinion later as time progresses).

The fist Quiz will be held in class on 13th Aug 2026 (Thu). Please attend classes seriously.

Reading Assignments (for your own benefit)

Suggested Reading 1

Practice Assignment 1

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