Scientific Computing (using Fortran)
Schedule
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Course Materials
Primarily three sources shall be used:
- F.S. Acton, Numerical methods that work, Harper and Row Publishers,
New York, Evanston and London, 1970. This is a beautiful book. I have the edition from
1970, the 1990 edition is available at the mathematics library of Stockholm Univeristy.
- W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes
in Fortran, Cambridge University Press, Cambridge, 1992. A very well-known and well-used
book in physics community. If you do not already have it, this may be a very useful book to
buy.
- D. Knuth, The Art of Computer Programming, Addison-Wesley
publishing company, Reading, Massachusetts. The authoritative guide to computer programming.
This book will not be used much in the course, except is some special topics, e.g.,
generation of random number, multiple-precision arithmatic.
if you are serious about scientifi computation it is absolutely necessary that
you are aware of these classics. Also have a look at Don Knuth's
webpage .
A very similar course from which I have borrowed quite a number of ideas is delivered by
Ake Nordlund. His website earlier had links
to a similar course.
Individual lectures are linked below :
Exam: About 40% on homeworks and 60% on a final exam. The form of the final exam is not fixed. It may even be a project.
Syllabus: The following topics are going to be covered. There may be some additions depending on students interest.
- Errors, Floats, precision arithmatic
- Matrices, diagonalisations, inversions.
- Integration
- Interpolation and extrapolation
- Extremization.
- Solution of (linear and non-linear) ODEs with di erent schemes, con-
servation laws, stiff equations.
- Random numbers
- FFT
- basic of PDEs
- Computation and hardware
In addition there will be some introduction to GPU computation.
I have given a similar course couple of years back. You can get a better idea of this
course by looking at the (incomplete) lecture notes of the earlier course
here.
We shall take a hands on approach. It is necessary that the students have their own laptops where they can run the programs in class.
Programs shall be shared using google drive. It will be useful if the students have a google account.
Preferred language of the course will be Fortran, although the students are welcome to use any other language (e.g., C, C++ ) to solve the exercises.