This page contains the program of the course. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.

The course will be given entirely online. Video lectures will be made available here on Canvas on at the same dates and times as the scheduled lectures in TimeEdit:

Video lectures

Discussions on the lectures will be held through the online forum Piazza.com. To sign up for our private classroom in Piazza, follow this link:

Sign up for Piazza here

Program

The schedule of the course is in TimeEdit.

We will cover most of the first 10 chapters of the book (see course-PM for info on the literature), except for chapter 6 which is omitted. The main point of the course is the careful introduction of the notions of differential forms, De Rham cohomology, manifolds, and vector fields, leading up to Stokes' theorem. Stokes' theorem is a general theorem on integration of differential forms on manifolds with boundaries, containing as special cases Green's formula, the divergence theorem and, yes, 'Stokes' theorem' for surfaces bounded by a curve in three-dimensional space. The difficulty in the subject is not so much the proof of this very central result as the build-up of the abstract notions in its statement.

Study guide for the exam

Rough course outline:

(the numbering is not in one-to-one correspondence with the chapters in the book)

0. Motivation

1. Recap from multivariable calculus 

2. Alternating algebra 

3. Differential forms 

4. de Rham cohomology 

5. Smooth manifolds

6. Differential forms on manifolds

7. de Rham cohomology of manifolds

8. Examples of de Rham cohomology

9. Integration on manifolds

 

 

Recommended exercises:

Chapter 1: 1.1, 1.2

Chapter 2: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.9, 2.10

Chapter 3: 3.1, 3.2, 3.3

Chapter 8: 8.2, 8.4, 8.5, 8.6

 

 

Back to the top

 

 

Reference literature:

1. Learning MATLAB, Tobin A. Driscoll. Provides a brief introduction to Matlab to the one who already knows computer programming. Available as e-book from Chalmers library.
2. Physical Modeling in MATLAB 3/E, Allen B. Downey
   The book is free to download from the web. The book gives an introduction for those who have not programmed before. It covers basic MATLAB programming with a focus on modeling and simulation of physical systems.

 

Back to the top