Homework Solution Differential Geometry Finance

Announcement

  • (Dec 8) Solution to Homework 11 is posted.
  • (Dec 1) The final exam will be held on Dec 15, 2016, 9:30am - 12pm at New Asia College Gymnasium. It will cover everything from the first lecture up to and including the lecture on Nov 29, and all the assignments. Please remember to bring your student ID to the exam. (Note: The Gauss and Codazzi equations will be given in the exam so you do not have to memorize them.)
  • (Nov 29) The deadline for Homework 11 is extended to Dec 6 at 5PM.
  • (Nov 23) Solution to Homework 10 is posted.
  • (Nov 22) The last Homework 11 is posted and it is due on Dec 1 (Thurs) at 5PM.
  • (Nov 17) Solution to Homework 9 is posted.
  • (Nov 15) Homework 10 is posted and it is due on Nov 22 (Tue) at 5PM.
  • (Nov 10) Solution to Homework 8 is posted.
  • (Nov 8) Homework 9 is posted and it is due on Nov 15 (Tue) at 5PM.
  • (Nov 3) Q.4 in Homework 8 has be corrected (Thanks to Wong Wing Hong for pointing out the mistake.)
  • (Nov 3) Solution to Homework 7 is posted.
  • (Nov 1) Homework 8 is posted and it is due on Nov 8 (Tue) at 5PM.
  • (Oct 27) Solution to Homework 6 is posted.
  • (Oct 25) Homework 7 is posted and it is due on Nov 1 (Tue) at 5PM.
  • (Oct 25) Midterm has been returned after class today. Here are the statistics: max=39, mean=27.3, median=28, standard deviation=8.08. If you missed class today, please pick it up from me after class on Thursday.
  • (Oct 18) Homework 6 is posted and it is due on Oct 25 (Tue) at 5PM.
  • (Oct 12) Solution to Homework 5 is posted.
  • (Oct 11) There is no homework posted this week in view of the coming midterm on Thursday.
  • (Oct 6) Solution to Homework 4 is posted.
  • (Oct 6) The midterm will be on Oct 13 in class (10:30am-12pm, LSB C2). It will cover materials up to and including the lecture on Oct 6 (excluding the differential topology of surfaces).
  • (Oct 4) Homework 5 is posted and it is due on Oct 11 (Tue) at 5PM.
  • (Sep 29) Solution to Homework 3 is posted.
  • (Sep 27) Homework 4 is posted and it is due on Oct 4 (Tue) at 5PM.
  • (Sep 22) Solution to Homework 2 is posted.
  • (Sep 20) Homework 3 is posted and it is due on Sep 27 (Tue) at 5PM.
  • (Sep 19) Solution to Homework 1 is posted.
  • (Sep 13) Homework 2 is posted and it is due on Sep 20 (Tue) at 5PM.
  • (Sep 7) Homework 1 has been revised.
  • (Sep 6) Homework 1 is posted and it is due on Sep 13 (Tue) at 5PM.
  • (Sep 6) There will no tutorial class in the first week. The first tutorial will begin on Sep 15.

General Information

Lecturer

  • LI Man-chun Martin
    • Office: LSB 236
    • Tel: 3943 1851
    • Email:

Teaching Assistant

  • CHAU Chi Fai
    • Office: LSB 222B
    • Tel: 3943 7963
    • Email:
    • Office Hours: Mon 8:30-11:30AM; Tue 8:30-10:30AM; Thurs 8:30-10:30AM, 1:30-2:30PM

Time and Venue

  • Lecture: Tu 10:30AM - 12:15PM, LSB C2; Th 10:30AM - 11:15AM, LSB C2
  • Tutorial: Th 11:30AM - 12:15PM, LSB C2

Course Description

This course covers basic theory on curves, and surfaces in the Euclidean three space. Topics include: regular curves, Frenet formulas, local theory of curves, global properties of curves such as isoperimetric inequality, regular surfaces, 1st and 2nd fundamental form, Gaussian curvature and mean curvature, Gauss map, special surfaces such as ruled surfaces, surfaces of revolution, minimal surfaces, intrinsic geometry: geodesic, and Gauss-Bonnet Theorem. Students taking this course are expected to have knowledge in advanced calculus, linear algebra, and elementary differential equations.


Textbooks

  • "Differential Geometry of Curves and Surfaces" by M. do Carmo, Prentice Hall 1976

References

  • "Curves and Surfaces (2nd ed)" by S. Montiel and A. Ros, Graduate Studies in Mathematics, Vol.69, American Mathematical Society, 2009
  • "Differential Geometry: Curves - Surfaces - Manifolds (2nd ed)" by W. Kuhnel, Student Mathematical Library, Vol.16, American Mathematical Society 2005
  • "Differential Forms and Applications" by M. do Carmo, Universitext, Springer-Verlag 1998

Pre-class Notes


Lecture Notes


Tutorial Notes


Assignments


Solutions


Assessment Scheme

Homework 10%
Midterm (Oct 13, in class) 40%
Final Exam 50%

Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

http://www.cuhk.edu.hk/policy/academichonesty/

and thereby help avoid any practice that would not be acceptable.


Last updated: December 08, 2016 22:31:45

Announcement

  • Tutorial will begin on Sep 10.
  • Homework 1 is posted and due on Sep 15 at 5PM.
  • The lecture notes is posted. Please note that the lecture notes will be revised continuously as the class goes on.
  • Homework 2 is posted and due on Sep 23 (Wed) at 5PM.
  • Midterm 1 will take place in the second half of the class next Tuesday (Sep 22). It will cover all the materials up to and including the lectures and tutorials this Thursday (Sep 17). There will still be lecture in the first half of the class before the midterm.
  • Homework 2 typo: #5, the power on the right hand side should be "n-i" instead of "n-1".
  • Homework 3 is posted.
  • The statistics for midterm 1 is as follows: mean=11.05, median=11, highest=16, standard deviation=3.23. If you have not got back your midterm, please come to my office to pick it up.
  • Homework 4 is posted.
  • There is a mistake in HW4 Q2 (b). The revised version has been uploaded.
  • Midterm 2 is changed to Oct 27 (Tuesday) in class. Please make sure to attend the midterm.
  • Homework 5 is posted.
  • The due date of Homework 5 is postponed to Oct 15.
  • For question 2 in HW5, the curve is arc-length parametrized. The revised version has been uploaded.
  • Homework 6 is posted.
  • In HW5 Suggested Exercise 1(a), the sign in front of epsilon should be "plus". The revised version has been uploaded.
  • Homework 7 & 8 are posted. Please note that HW 7 is due on Wednesday, the day after midterm 2.
  • Midterm 2 will be held in class on Oct 27, 10:30-11:30AM. There will be no lecture on that day. The test will cover all the materials up to and including the lecture on Oct 22.
  • In Q.1 of Homework 6, there should be no "squared" of the integrand. The revised version has been uploaded.
  • Homework 9 is posted.
  • Midterm 2 has been returned in class today. Here are the statistics: mean = 17.3, median = 18, standard deviation = 2.63. If you missed class today, please come to my office to pick up your midterm.
  • In suggested solution to HW 7 Q.3(b), the semi-circles need to be reparametrized suitably to satisfy the geodesic equations.
  • The final exam has been scheduled on Dec 15, 2015 (Tuesday) 9:30am - 12:00pm at Indoor Multi-purpose Sports Hall, Shaw College. Please refer to the RGS webpage for the most up-to-date information.
  • Homework 10 is posted.
  • The last homework assignment 11 is posted. Please note that the due date is on Nov 26, Thursday.

General Information

Lecturer

  • Li Man-chun Martin
    • Office: LSB 236
    • Tel: 3943-1851
    • Email:

Teaching Assistant

  • Huang Shaochuang
    • Office: LSB 222A
    • Tel: 3943-3575
    • Email:
    • Office Hours: Tu 1:30-6:15PM, W 8:30AM-12:15PM, F 8:30AM-12:15PM
  • Wang Qizhi
    • Office: LSB 233
    • Tel: 3943-7957
    • Email:
    • Office Hours: M 2:30-5:00PM, W 2:30-5:00PM, F 8:30AM-12:00PM

Time and Venue

  • Lecture: Tu 10:30AM - 12:15PM, LSB C2; Th 10:30AM - 11:15AM, LSB C2
  • Tutorial: Th 11:30AM - 12:15PM, LSB C2

Course Description

This course covers basic theory on curves, and surfaces in the Euclidean three space. Topics include: regular curves, Frenet formulas, local theory of curves, global properties of curves such as isoperimetric inequality, regular surfaces, 1st and 2nd fundamental form, Gaussian curvature and mean curvature, Gauss map, special surfaces such as ruled surfaces, surfaces of revolution, minimal surfaces, intrinsic geometry: geodesic, and Gauss-Bonnet Theorem. Students taking this course are expected to have knowledge in advanced calculus, linear algebra, and elementary differential equations.


Textbooks

  • "Differential Geometry: Curves - Surfaces - Manifolds" (2nd edition) by Wolfgang Kuhnel

References

  • "Differential Geometry of Curves and Surfaces" by Manfredo do Carmo
  • "Differential Forms and Applications" by Manfredo do Carmo

Pre-class Notes


Lecture Notes


Tutorial Notes


Assignments


Solutions


Assessment Scheme

Weekly Homework Assignment 10%
Midterms (Sep 22 and Oct 27) 40%
Final Exam (Dec 15 9:30AM-12:00PM, please refer to RGS's webpage for the most updated information) 50%

Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

http://www.cuhk.edu.hk/policy/academichonesty/

and thereby help avoid any practice that would not be acceptable.


Last updated: December 03, 2015 13:40:00

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