Introduction to numerical mathematics and modeling. Numerical interpolation, curve fitting,
integration and optimization. Data fitting and filtering. Solving systems of linear equations.
Basics of the Monte Carlo method. Computer exercises.
Timetable for Fall 2004
Lectures: Wednesdays at 14-16, lecture room S5
(Dept. of Electrical Eng.) (1st lecture Wed 15.9.)
Exercises: Mondays at 14-16 or Tuesdays at 16-18,
computer classroom Y339b (main building) (1st exercises Mon 27.9./ Tue 28.9.)
All the course material (lecture notes, exercise papers, etc) are in
english but the lectures are given in Finnish.
However, English speaking students are welcome to participate and
extra help sessions can be arranged if necessary.
Use wwwtopi to register for the course
(lectures only, no registration for the exercise groups).
To pass the course, both of the following requirements must be fulfilled:
Exercises: at least 50% of the exercises must be completed (grade 0-5).
Final exam: at least 50% of the total points (grade 0-5).
The final grade of the course will be calculated from the following
Lecture 5 Systems of linear equations (20.10.2004)
Lecture 6 Spline functions (27.10.2004)
Lecture 7 Smoothing of data and the method of least squares (3.11.2004)
Lecture 8 Random numbers (10.11.2004)
Lecture 9 Monte Carlo I (17.11.2004)
Lecture 10 Monte Carlo II (24.11.2004)
Lecture 11 Monte Carlo III / Review (8.12.2004 )
NOTE CHANGE OF SCHEDULE: Last lecture 8.12.2004 and no lecture 1.12.!
(Last exercise due 8.12., based on lecture 10)
NOTE: Error in lecture notes 4: Adaptive Simpson's algorithm!
The code given in the lecture notes is incorrect (p.103). Variables 'level' and 'eps'
should not be passed as pointers. Corrected code is here.
Note: You can compile the Fortran 77 code using Fortran 90/95.
NOTE: Exercise 10, Problem 1 (ISING MODEL / METROPOLIS):
In the Metropolis algorithm (lecture notes p256), the lattice array is named 'spin',
whereas earlier (p. 254-255) it is called 'lattice'. These two mean the same thing!
NOTE: Exercise 9, Problem 1:
Instead of calculating the average deviation (as described in the problem sheet),
you can also calculate the absolute error for the final estimate:
abs_err = |pi_est - pi_true|, and compare this to your calculated error estimate (std)
(as a function of N).
(Link to the lecture notes pages, same username and password required.)
Lecture notes (download the material here)
NOTE: The lecture notes are intended for students of this course only.
Username and password are required (given in the first lecture).
Please contact the lecturer if you do not know these.
Additional material (textbooks)
Numerical Mathematics and Computing,
4th edition, W. Cheney and D. Kincaid, Brooks/Cole (1999).
(Ch. 1-7, 10-11.)
Recommended! (Covers lectures 1-7).
Numerical Recipes in C or FORTRAN,
W. H. Press, S. A. Teukolsky, W. T. Vetterling, Brian P. Flannery,
Cambridge University Press (1993-1997).
BOOKS ON-LINE (Cornell University Library)
"The guide" of numerical analysis.
A Guide to Monte Carlo Simulations in Statistical Physics,
D. P. Landau and K. Binder, Cambridge University Press (2000).
A good textbook for those interested in MC methods.
Monte Carlo simulation in statistical physics : an introduction
K. Binder, D. W. Heermann, Springer (2002).
Another good Monte Carlo guide.
Understanding molecular simulation : from algorithms to applications
Daan Frenkel, Berend Smit, Academic Press (2002)
An extensive guide to MC and MD methods (applied to molecular simulation).
These are just suggestions. There are lots of other good books available too.
For example, try the following key words
in the HUT library search:
- numerical analysis (introduction)
- scientific computing
- C programming
CSC Center for Scientific Computing
Lots of useful information about scientific computing.
Also guides (e.g. a good online F95 guide).
Dr. Tech. Laura Juvonen
Helsinki University of Technology
Laboratory of Computational Engineering
P.O.Box 9203, FI-02015 TKK
tel: 451 5733