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

Program

The schedule of the course is in TimeEdit.

We will cover most of the first 10 chapters of the book, but we will treat 4-6 more superficially. 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 lectures or the chapters in the book)

1. Motivation and recap from multivariable calculus 

2. Alternating algebra 

3. Differential forms 

4. de Rham cohomology 

5. Manifolds

6. de Rham cohomology of manifolds

7. 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

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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.

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