SAYT1134 - Towards Differential Geometry - 2023/24

Announcement

• Test 1: Aug 16, 2024 (Friday) 2:30-4:00pm at MMW702,704,705,706 (Same as the usual Tutorial class)
• Test 1 Coverage: All lecture and tutorial materials up to the teaching content on 14/8, including all the exercises assigned or not assigned in homework.
• Test 1 statistics: Mean=42.33/80, Median=39/80, SD=17.98, Max=73/80, UQ=51/80, LQ=32/80
• Test 2: Aug 23, 2024 (Friday) 2:30-4:00pm at MMW702,704,705,706 (Same as the usual Tutorial class)
• Test 2 Coverage: All lecture and tutorial materials up to the teaching content on 21/8, from 2.1 (regular parametrized curves) up to 3.2 (1st fundamental form and surface area) and all the exercises assigned or not assigned in homework.
• Test 2 statistics: Mean=55.46/80, Median=53/80, SD=23.79, Max=92/80, UQ=61/80, LQ=40/80
• Final exam: August 30, 2024 (Friday) 10:30am-1:00pm, MMW702 703
• Final exam coverage: all material including those in lectures (including all test coverage up to test 2, and all contents up to 27/8, excluding 3.4.15 to 3.4.18 related to normal curvatures), all tutorial materials, exercises & homework, with emphasis on those material after the test 2 (i.e. Ch 3.2). But those material before the test 2 may also be tested directly/explicitly or indirectly/implicitly.
• Final Statistics: Mean=63.17/100, Median=62/100, SD=25.83, Max=110/100, UQ=72/100, LQ=47/100

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General Information

Lecturer

• Dr. Man Chuen CHENG
  • Office: LSB210
  • Email:
  • Office Hours: By appointment

Time and Venue

• Lecture: 10:30AM-1:15PM, MMW 702; MMW 703 (9/8, 26/8, 27/8 only)
• Tutorial: 2:00PM-5:15PM, MMW 702; MMW 704; MMW 705; MMW 706, LSB 222

Course Description

This course, combining the knowledge of calculus and geometric intuition, leads students to explore the fruitful variety of curves and surfaces beyond lines, planes, and conics. Students will use calculus up to partial differentiation to describe curves and surfaces, to calculate the tangent vector, normal vector and curvature, tangent plane, geodesic and Gaussian curvature. Other essential geometric theorems, such as Gauss-Bonnet, will be introduced.

References

• "Differential Geometry of curves and surfaces" by Manfredo P. do Carmo, 2nd edition, Dover
• "Linear Algebra" by Friedberg, S., 4th edition, Pearson
• "Thomas' Calculus" by Thomas, Weir & Hass, 14th edition, Pearson

Pre-class Notes

• Course Outline

Lecture Notes

• Lecture 1
• Lecture 2
• Lecture 3
• Lecture 4
• Lecture 5
• Lecture 6
• Lecture 7
• Lecture 8
• Lecture 9

Tutorial Notes

• Aug-09 Group 4 Exercises
• Aug-09 Group 2 Tutorial 1 (Revised on 18/08/2024)
• Aug-12 Group 1 Tutorial 2
• Aug-12 Group 2 Tutorial 2
• Aug-12 Group 3 Tutorial 2
• Aug-12 Group 4 Tutorial 2
• Aug-14 Group 2 Tutorial 3 (final revised at 11:25PM on 14/8)
• Aug-14 Group 3 Tutorial 3
• Aug-16 Group 2 Tutorial 4
• Aug-19 Group 2 Tutorial 5 (Revised on 20/08/2024)
• Aug-19 Group 3 Tutorial 5
• Aug-21 Group 2 Tutorial 6
• Aug-21 Group 3 Tutorial 6
• Aug-23 Group 1 Tutorial 7
• Aug-23 Group 2 Tutorial 7
• Aug-26 Group 1 Tutorial 8
• Aug-26 Group 2 Tutorial 8 (Revised on 26/08/2024)
• Aug-27 Group 1 Tutorial 9
• Aug-27 Group 2 Tutorial 9
• Aug-28 Group 2 Supplementary to Tutorial 9

Assignments

• Group 2 Exercise 1 (Revised on 18/08/2024)
• Group 2 Exercise 2
• Group 2 Exercise 3
• Group 2 Exercise 5
• Group 2 Exercise 6

Quizzes and Exams

• Past Paper: 2023 TDG Test 1
• 2024 TDG Test 1
• Past Paper: 2023 TDG Test 2
• 2024 TDG Test 2
• 2024 Final Exam

Solutions

• Group 2 Exercise 1
• Group 2 Tutorial 1
• Past Paper: 2023 TDG Test 1
• 2024 TDG Test 1
• Group 2 Exercise 2
• Group 2 Exercise 3
• Past Paper: 2023 TDG Test 2
• Group 2 Exercise 5
• 2024 TDG Test 2
• Group 2 Exercise 6 (revised on 28/8)

Assessment Scheme

Classwork		10%
Test 1 (Aug 16, 2:30PM-4:00PM, in-class)		20%
Test 2 (Aug 23, 2:30PM-4:00PM, in-class)		20%
Final Exam (Aug 30, 10:30AM-1:30PM, in-class)		50%

Useful Links

• Videos (by students' requests)

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Assessment Policy

Last updated: September 02, 2024 11:11:57