Embedded Files
Announcements:
20) Answer sheets of the final exams will be shown tomorrow from 2:00 PM in AB2-5A. Please check email for details.
19) Solution to the final exam uploaded.
18) Solution to HW11 and some notes on last week's classes (curvature.pdf) uploaded.
17) HW11 and solution to HW10 are uploaded.
16) Solution to Midterm 2 uploaded.
15) HW10 uploaded.
14) Solution to HW9 uploaded.
13) HW8 uploaded.
12) There is an error in Qn 2 of HW7.
11) HW7 uploaded.
10) Solution to HW6 uploaded.
9) Solutions to HW5 and midterm1 uploaded; HW6 uploaded.
8) HW5 and solution to HW4 uploaded.
7) HW4 uploaded.
6) Solution to Homework 2 and Homework 3 uploaded.
5) There will be a quiz tomorrow 21/8/19 during tutorial. It is on computing derivatives.
4) Please note that links to each HW and solution will be deleted after one week.
3) HW2 uploaded.
2) Solution keys to HW1 uploaded.
1) HW 1 uploaded. Check below.
Course Outline:
Differentiation of vectors.
Curves in the plane and in space, arc length, reparametrization.
Curvature, torsion, Serret-Frenet formulae.
Fundamental theorem of curves in plane and space.
Surfaces in three dimension (2-manifolds), smooth surfaces.
Tangents, normals, quadratic surfaces.
Change of variable formula, surfaces of revolution.
First and second fundamental forms, isometries, conformal mappings.
Normal and principal curvatures, Gaussian curvature and the Gauss map.
Geodesics, geodesic curvature, Gauss' theorema egregium.
Additional Topics
Isoperimetric inequality, four vertex theorem.
Area and volume integrals, surface area.
Pre-requisites: Students who have done a course in calculus and a course in co-ordinate geometry before will have advantage.
Text book: A. Pressley, Elementary Differential Geometry, SUMS, Springer (2001).
Homework: One homework set will be assigned every week. It will be posted in this web page. However, no homework will be collected or graded.
Exams and Quizzes: There will be two midterms and one final exam. I plan to conduct two quizzes per month. Quizzes will be held during the tutorial
sessions.
Grades: Quizzes 20%, Midterm 20% each, Final 40%.
Attendance: Before any of the exams if your attendance falls below 70% then you won't be allowed to write that exam. If by mistake you are found to
have attendance below 70% only after the exam then your test will not be graded.
Link to HW: See below. Each HW link will be deleted after one week.
Page updated
Google Sites
Report abuse