01234 Differential Geometry with Applications

Spring Semester F12

Course info


Teacher: Steen Markvorsen, Department of Mathematics
                Building 303 South East Wing, Room 052
                S.Markvorsen@mat.dtu.dk

 

Teaching assistant:  Jakob Møller-Andersen, s082754@student.dtu.dk

 

 


Course Schedule: F2B : Thursdays from 8:00 to 12:00, first time: Thursday February 2nd

Auditorium: Building 306,  Auditorium 33

Exercises take place in: Building  303 South East section, hall way, room 034, and room 043 (Matematicum)

Course Language: English

 

Tentative program (under construction)

Textbook: [P]: Andrew Pressley, Elementary Differential Geometry, Second Edition, Springer, 2010
NB: From the marked link you have free access to the full *.pdf version of the textbook.
The book is also available from the Polytechnic Bookstore, DTU.

The full system of numbered exercises are available via CampusNet file share folder EXERCISES.

Week 01

Feb. 02

[P] Chapter 1: Curves in Plane and in Space

Exercises:  [P]:  1.1.1, 1.1.2, 1.1.6, 1.1.8, 1.2.1, 1.2.2, 1.2.3, 1.2.4, 1.3.1, 1.5.6 (selected brief solutions are also in [P]). Exercises in red are a bit more theoretically oriented than the others.
Quiz00 (Free prototype sample quiz - not valid for credit, you can hand it in next week), see CampusNet
Homework (valid for partial credit) for next week: Set 01, see CampusNet

Week 02

Feb. 09

[P] Chapter 2: How much does a Curve curve?

Exercises: 2.1.1, 2.2.1, 2.2.15, 2.3.1, 2.3.3, 2.3.4, 2.3.9, 2.3.13, 2.3.14

Hand in free Quiz00
Hand in Homework Set 01

Week 03

Feb. 16

[P] Chapter 4: Surfaces in three Dimensions

Exercises:  4.1.6, 4.1.4 (first question), 4.1.8, 4.2.3, 4.2.16, 4.4.1, 4.4.5
Homework (valid for partial credit) for next week: Set 02, see CampusNet

Week 04

Feb. 23

[P] Chapter 5: Examples of Surfaces

Exercises: 5.1.1, 5.2.2, 5.3.1, 5.3.2, 5.4.1

Quiz 1 (Valid for credit)
Hand in Homework Set 02

Quiz 1

Thursday, Feb. 23

Quiz 1 from 8:00 to 8:45 in auditorium 33, Bldg. 306

Quiz 1 from 8:00 to 8:45

Week 05

Mar. 01

[P] Chapter 6: The First Fundamental Form

Exercises: 6.1.1, 6.1.7, 6.2.1, 6.2.2 (optional), 6.3.2, 6.4.1 (optional), 6.4.2, 6.4.12

Homework (valid for partial credit) for next week: Set 03, see CampusNet

Week 06

Mar. 08

[P] Chapter 7: Curvature of Surfaces

Exercises: 7.1.1, 7.1.2, 7.1.5 (optional), 7.2.2 (optional), 7.3.2, 7.3.3, 7.3.10, 7.3.11
Hand in Homework Set 03

Week 07

Mar. 15

[P] Chapter 8: Curvatures, Mean, Gaussian, and Principal

Exercises: 8.1.2, 8.1.11, 8.1.1, 8.2.10, 8.5.1, 8.5.2, 8.2.12
Homework (valid for partial credit) for next week: Set 04, see CampusNet

Week 08

Mar. 22

[P] Chapter 9: Geodesics,

Shortest Curves

Exercises: 9.1.3, 9.1.1 (optional), 9.1.7, 9.1.13, 9.2.3 (important), 9.3.1 (optional), 9.3.5, 9.3.7, 9.3.8
Quiz 2 (Valid for credit)
Hand in Homework Set 04

Quiz 2

Thursday, Mar. 22

Quiz 2 from 8:00 to 8:45 in auditorium 33, Bldg. 306

Quiz 2 from 8:00 to 8:45

Week 09

Mar. 29

[P] Chapter 10: Theorema Egregium,

Gauss’ Fantastic Theorem

Exercises: 10.1.2, 10.1.4, 10.2.1 (optional),10.2.9, 10.2.10, 10.2.5, 10.2.7
Homework (valid for partial credit) for next week (week 10): Set 05, see CampusNet



 

Easter Holidays Apr. 02. - Apr. 09.

Week 10

Apr.12

[P] Chapter 13: The Gauss-Bonnet Theorem

Exercises: 13.2.1, 13.2.2, 13.2.3, 13.4.3, 13.4.4, 13.5.4, 13.5.5 (optional)
Hand in Homework Set 05

Week 11

Apr. 19

Quiz 3 and Workshop

Quiz 3 (Valid for credit) and prepare for project exercise

Quiz 3

Thursday, April 19

Quiz 3 from 8:00 to 8:45 in auditorium 33, Bldg. 306

Quiz 3 from 8:00 to 8:45

Week 12

Apr. 26

Work on individually chosen Project-Exercises

Week 13

Apr. 03

Work on individually chosen Project-Exercises

Exam Period

May 16

Deadline for Project Reports

Wednesday, May 16 at 16:00



 

Further References