# 01234 Differential Geometry with Applications

## Course info

Teacher: Steen Markvorsen, DTU Compute
Building 303 South East Wing, First Floor, Room 160
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 7th

Auditorium: Building 306,  Auditorium 35

Exercises take place in: Building  302 Area H00NØ (North East Ground Floor Area)

Course Language: English

## Tentative program (under construction)

Textbook: [P]: Andrew Pressley, Elementary Differential Geometry, Second Edition, Springer, 2010

The soft covered paper based book is also available from the Polytechnic Bookstore, DTU.

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

 Week 01 Feb. 07 [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 (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), see CampusNet Homework (valid for partial credit) for next week: Set 01, see CampusNet Week 02 Feb. 14 [P] Chapter 2: How much does a Curve curve and twist? Exercises: 2.1.1, 2.1.3, 2.2.1, 2.2.15, 2.3.1, 2.3.4, 2.3.9 Hand in Homework Set 01 Week 03 Feb. 21 [P] Chapter 4: Surfaces in three Dimensions Exercises:  4.1.6, 4.1.4 (first question), 4.1.8, 4.2.3 (optional), 4.2.16, 4.4.1, 4.4.5 Homework (valid for partial credit) for next week: Set 02, see CampusNet Week 04 Feb. 28 [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. 28 Quiz 1 from 8:00 to 8:45 in auditorium 35, Bldg. 306 Quiz 1 from 8:00 to 8:45 Week 05 Mar. 07 [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. 14 [P] Chapter 7: Curvature of Surfaces Exercises: 7.1.1, 7.1.2, 7.1.5, 7.2.2, 7.3.2, 7.3.3, 7.3.10, 7.3.11 Hand in Homework Set 03 Week 07 Mar. 21 [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 Easter Holidays March 25. – April 1. Week 08 Apr. 04 [P] Chapter 9: Geodesics, Shortest Curves Exercises: 9.1.3, 9.1.1, 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, Apr. 04 Quiz 2 from 8:00 to 8:45 in auditorium 33, Bldg. 306 Quiz 2 from 8:00 to 8:45 Week 09 Apr. 11 [P] Chapter 10: Theorema Egregium, Gauss’ Fantastic Theorem Exercises: 10.1.2, 10.1.4, 10.2.1, 10.2.5, 10.2.7, 10.2.10 Homework (valid for partial credit) for April 25. (week 11): Set 05, see CampusNet Week 10 Apr.18 [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) Homework Set 05 for next week: Set 05, see CampusNet Week 11 Apr. 25 Quiz 3 and Workshop Quiz 3 (Valid for credit) and prepare for project exercise Hand in Homework Set 05 Quiz 3 Thursday, April 25 Quiz 3 from 8:00 to 8:45 in auditorium 33, Bldg. 306 Quiz 3 from 8:00 to 8:45 Week 12 May 02 Work on individually chosen Project-Exercises Holidays May 9. – May 10. 25. Week 13 May 16 Work on individually chosen Project-Exercises Exam Period May 29 Deadline for Project Reports Wednesday, May 29. at 16:00

## Further References

• M. P. DoCarmo, Differential Geometry of Curves and Surfaces , Prentice Hall, 1976
• A. Gray, Modern Differential Geometry of Curves and Surfaces with Mathematica, Second Edition, CRC Press New York, 1998
• J. J. Koenderink, Solid Shape, MIT Press, Cambridge, Massachusetts, 1990
• W. Kühnel, Differential Geometry: Curves - Surfaces - Manifolds, Second Edition, American Mathematical Society, 2006
• R. S. Millman and G. D. Parker, Elements of Differential Geometry, Prentice Hall, 1977
• S. Montiel and A. Ros, Curves and Surfaces, American Mathematical Society, 2005
• J. Oprea, Differential Geometry and its Applications, Prentice Hall, 1997
• C. Bär, Elementary Differential geometry, Cambridge, 2010
• T. Banchoff and S. Lovett, Differential Geometry of Curves and Surfaces, A. K. Peters Ltd., 2010
• D. J. Struik, Lectures on Classical Differential Geometry, Second Edition, Dover, 1961
• J. J. Koenderink, Solid Shape, MITPress, 1990
• H. Pottmann, A. Asperl, M. Hofer, and A. Kilian, Architectural Geometry, Bentley Institute Press, 2007