Numerical Methods I

The course covers the standard techniques of numerical computation from a theoretical as well as a practical perspective, including aspects of large-scale high-performance computation, and provides the foundation for more specialized third year courses in computation and modeling.

It is assumed that participants have the mathematical background equivalent to two semesters of Engineering and Science Mathematics - attendance of the first year B track (Multivariable Calculus, ODE; Linear Algebra, Fourier Methods, Probability) is highly recommended but not formally required - or Analysis I/II and Linear Algebra I. Familiarity with Matlab (or Octave) is an asset but not a prerequisite.

The course is appropriate as a home school elective for students of all majors with a particular interest in computation. It is recommended that students commit to this course for the full year. Students interested in a more compact introduction to methods of numerical computation are advised to take the one-semester Engineering and Science Mathematics 4A (Numerical Methods) instead.

Topics covered throughout the year are: computer arithmetic, condition of algorithms, systems of linear equations including iterative methods, computation of eigenvalues, interpolation and least square methods, numerical integration, numerical solution of ordinary differential equations, optimization techniques, and probabilistic aspects in computation.

Lectures:	W 8:15- 9:30 in East Hall 4	F 9:45-11:00 in East Hall 4
Lab:	CLAMV Teaching Labs 112/113 Research I (first meeting on We 9/8, 19:15)

• E. Süli, D. Mayers: Introduction to Numerical Analysis, Cambridge University Press, 2003.
• A. Quarteroni, F. Saleri: Scientific Computing with MATLAB, Springer, 2003.

• A. Quarteroni, R. Sacco, F. Saleri: Numerical mathematics, Springer, 2000.
• J. Stoer, R. Bulirsch: Introduction to numerical analysis, 3rd edition, Texts in Appl. Math., vol. 12, Springer, 2002.
• P. Deuflhard, A. Hohmann: Numerical analysis in modern scientific computing, 2nd edition, Texts in Appl. Math., vol. 43, Springer, 2003.
• P. Deuflhard, F. Bornemann: Scientific computing with ordinary differential equations, Springer, 2002.

The solutions to the weekly homework and project sheets handed out in week X need to be turned in before the Friday lecture in week X+1. Code should be sent in a single email to Christian Kuehn . You should be able to present and explain the code in the lab session following submission.

Homework is your individual work. Collaborative project work in groups of two or three is permissible provided:

• Each member of the group maintains and submits their own runnable version of the code.
• You state who you collaborated with (e.g. as comments in the source files).
• Each member of the group is able to explain the code without help from others.

You may consult books and internet resources, provided you always quote the source.

• The final grade will be computed from the weighted average of percentages of maximal scores with the weights

  Homework:	15%
  Projects:	30%
  Midterm Exam:	15%
  Final Exam:	40%

  
  according to the following table:

  Cutoff score:	95%	90%	85%	80%	75%	70%	65%	60%	55%	50%	45%	40%
  IUB Points:	1.0	1.33	1.67	2.0	2.33	2.67	3.0	3.33	3.67	4.0	4.33	4.67