Instructor | Joj Helfer | TA | Zijian Rong |
jhelfer (at) usc (dot) edu | zijianro (at) usc (dot) edu | ||
Office Hours | MWF 12-1pm, by appointment (in KAP 464-B) | Office hours | T 1-3pm and W 5-6pm (in the Math Center, KAP 263) |
All announcements will be posted on Blackboard.
You can find a brief outline of the lectures here.
Here are the notes for just Lecture 42.
Homework 13
has been posted.
It is due on Wednesday, April 24.
See the Homework page for older homework assignments.
This course will apply advanced topics in calculus to differential geometry, which is the study of curves in the plane and of curves and surfaces in space, as well as of manifolds, which are higher-dimensional analogues of curves and surfaces.
In the first half of the course, we will be going through more or less all of Michael Spivak’s classic book Calculus on Manifolds. This will in part be a review of the main concepts from multivariable calculus: partial derivatives, the Jacobian matrix, and multi-dimensional integration. We will then introduce the conept of differential form, which provide an extremely elegant geometric reformulation of integration theory.
We will then introduce manifolds and differential forms on manifolds. The culmination of this part of the course is the differential forms version of Stokes’ Theorem, which includes as special cases the classical Stokes’ Theorem, as well as Green’s Theorem and the Divergence Theorem, and generalizes these to manifolds of all dimensions.
In the second half of the course, we will turn from the general theory of manifolds, to the study of curves and surfaces, following (parts of) Kristopher Tapp’s book Differential Geometry of Curves and Surfaces.
The main emphasis of this part of the course will be the notion of curvature, and it will culminate with the Gauss-Bonnet Theorem, which relates the curvature of a surface to its topology, that is, to its overall shape.
For a more detailed (preliminary) week-by-week list of topics to be covered, please see the lecture plan here.
In the first part of the course, we will be following
After that, we will be following
Multivariable calculus (including multivariable integration) and linear algebra.
The official prerequisites are: at least one of Math 226, Math 227, or Math 229, and at least one of Math 225 or Math 245.
Most information and material related to the course will be posted on this page.
The exceptions are:
Homework assignments will be assigned every week.
Homework is to be submitted on Gradescope (you should see the course there if you are enrolled; if you have any problems, please inform the instructor or TA). When you submit on Gradescope, please don’t forget to match your scanned pages with the problems.
Homework must be submitted by the posted due dates. If you expect to have issues submitting the homework on time, or if you are having difficulties with gradescope, please write to the instructor or TA as soon as possible, and attach a scanned copy of your submission (this is a wise practice for any class).
You are encouraged though not required to type up your homework using LaTeX. If you do not have experience with LaTeX and would like to learn how to use it, please ask the instructor or TA.
Both exams are closed book, closed notes exams, with no calculators or other electronic aids permitted. The final exam will cover all topics from the semester, but will have greater emphasis on topics developed after the midterm.
The TA’s and instructor’s office hours are TBA.
Any student requesting academic accommodations based on a disability is required to register with Disability Services and Programs (DSP) each semester A letter of verification for approved accommodations can be obtained from DSP. Please be sure the letter is delivered to me (or to TA) as early in the semester as possible. DSP is located in GFS 120 and is open 8:30 a.m.–5:00 p.m., Monday through Friday. Website for DSP (https://dsp.usc.edu/) and contact information: (213) 740-0776 (Phone), (213) 740-6948 (TDD only), (213) 740-8216 (FAX) dspfrontdesk@usc.edu.
USC seeks to maintain an optimal learning environment. General principles of academic honesty include the concept of respect for the intellectual property of others, the expectation that individual work will be submitted unless otherwise allowed by an instructor, and the obligations both to protect one’s own academic work from misuse by others as well as to avoid using another’s work as one’s own. All students are expected to understand and abide by these principles. SCampus, the Student Guidebook, contains the University Student Conduct Code (see University Governance, Section 11.00), while the recommended sanctions are located in Appendix A.
USC seeks to maintain an optimal learning environment. General principles of academic honesty include the concept of respect for the intellectual property of others, the expectation that individual work will be submitted unless otherwise allowed by an instructor, and the obligations both to protect one’s own academic work from misuse by others as well as to avoid using another’s work as one’s own. All students are expected to understand and abide by these principles. SCampus, the Student Guidebook, contains the University Student Conduct Code (see University Governance, Section 11.00), while the recommended sanctions are located in Appendix A.
In case of a declared emergency if travel to campus is not feasible, USC executive leadership will announce an electronic way for instructors to teach students in their residence halls or homes using a combination of Blackboard, teleconferencing, and other technologies. See the university’s site on Campus Safety and Emergency Preparedness.
This syllabus is not a contract, and the Instructor reserves the right to make some changes during the semester.
Problem sets will be posted here each week.
You can find solutions to old problem sets on Blackboard
Due date | Assignment |
---|---|
Wed, Jan. 17 | Homework 1 |
Wed, Jan. 24 | Homework 2 |
Wed, Jan. 31 | Homework 3 |
Wed, Feb. 7 | Homework 4 |
Wed, Feb. 14 | Homework 5 |
Wed, Feb. 21 | Homework 6 |
Wed, Mar. 6 | Homework 7 |
Wed, Mar. 20 | Homework 8 |
Wed, Mar. 27 | Homework 9 |
Wed, Apr. 3 | Homework 10 |
Wed, Apr. 10 | Homework 11 |
Wed, Apr. 17 | Homework 12 |
Wed, Apr. 24 | Homework 13 |