MTH 201(Summer 2020)

MTH201: Curves and Surfaces

[Cr: 3, Lc: 2, Tt: 1, Lb: 0]

Announcements:

(4) Instructions for exam on Wed 5/8/20:

This will be a paper exam. Here are the details:

The exam will be held online using zoom as well as moodle. There will be three parts of the exam. Part A: This will consist of 10 short answer type questions worth 20 points. One has to do these in 30 minutes and then scan and submit through moodle. For this there will be a 10 min window. Then part B and part C will be of 40 points each which will have broad answer type questions. In part B you will be asked on plane and space curves. In part C you will be asked about surfaces. There will be a 15 min window after part B exam during which you are supposed to scan and submit your answers through moodle and use the restroom. After the part C you will have a 10 min window to scan and submit the answer sheets again through moodle.

Note: 0) Try to make sure that your internet connection is stable.

1) Make a black and white scan so the file size is relatively smaller and easier for you to upload.

2) You need to be logged in all the while through zoom for which I will send you link on the day of the

exam. You need to login through zoom at 2:00PM sharp. You will be directed to join your respective

breakout room by invigilators. Then we will start the exam at 2:10.

3) Question paper for one part will be shared with you after the exam of the earlier part is over.

4) Nobody will be allowed to take extra time.

5) At any point if we feel suspicious then I reserve the right to ask you about the clarification

of certain part(s) of the exam on Thursday. We will record the exam on zoom. So all people

must keep their video on. Please make sure that you choose a quiet place at home to write the

exam.

6) Summary: Part A: 2:10-2:40, Part B: 2:50-3:50, Part C: 4:05-5:05. Exam will be over by 5:15.

(3) I will hold tutorial sessions on skype

sometimes towards the end of the month. I will let you know two

days before the tutorial. It will be a 2 hour session or something

like that. All the HW and their solutions are here:

https://github.com/IISERM/course_files/tree/master/Math/201/ms18/Assignments%20-%202019

(2) Please note that there will be only one final exam

and no other exams or HW or quizzes. The logistics to conduct such

an exam will be clarified later. The exam will be held towards the end of

the 1st week of August, 2020 as per Dean Academics guidelines.

It will be a three hour exam.

Old announcements:

(1) Please download all the HW sets posted below.

They will be replaced by a new set of HW in two days. (2) Syllabus

and a study guide are posted below too.

Syllabus and study guide: The following topics will be on the syllabus

• • Differentiation of vectors.

  • Curves in the plane and in space, arc length, parametrization.

  • Curvature, torsion, Serret-Frenet formulae (only statement).

  • Fundamental theorem of curves in plane and space (only statement)

  • Surfaces in three dimension, smooth regular surfaces, basic examples of surfaces.

  • Tangent, normal.

  • Surfaces of revolution.

  • Gaussian curvature and the Gauss map.

Roughly: Chapter 1, 2, 4(4.1-4.4), 5(5.1-5.3, skip ruled surface), 6(6.1, 6.2)

and 7.2 of the text book.

A study guide: Make sure that you know all the basic definitions e.g.

regular curves, curvature of curves (not the just the formula), surfaces etc.

Long and complicated proofs of theorems will not be asked in the exams.

You should go through all the examples worked out the text book or notes that

you may have from the last course you attended. Solve all the problems from

the HW sets and as many problems from the text book as possible. Also

statements of important theorems may be asked in the exam. Send an email

if you have questions.

Pre-requisites: Students must have done a course in calculus and a course in co-ordinate geometry.

Text book: A. Pressley, Elementary Differential Geometry, SUMS, Springer (2001).

Homework: See below.

Exams and Quizzes: As per dean academic's guidelines.

Grades: TBA

Link to HW: