SUMMER RESEARCH PROGRAM FOR UNDERGRADUATES 2007
Program Description
This is a program in Applied Mathematics.
This year, it features:
- An intensive course in "Advanced
numerical methods
in Applied Mathematics".
- Research project.
- Labs in Matlab programming.
- Regular seminars on different topics in Applied Mathematics.
- Social activities.
Course
description for 2007
The course "Advanced numerical methods in Applied Mathematics" will cover the following topics:
Research Description for 2007.
The research problems to be considered will be related to the following topics:
Faculty in the program
The course "Advanced numerical methods in Applied Mathematics" will cover the following topics:
- Numerical Linear Algebra:
Error analysis and conditioning.
- Floating point arithmetic.
- Conditioning and stability
- LU factorization and Linear
Systems: error analysis, sensitivity of the LU factorizations,
structured problems.
- Tridiagonal systems.
- Cholesky factorization.
- Dynamical systems and applications
- Existence and uniqueness.
- Dependence of the initial conditions and parameters.
- Wellposedness.
- Linear stability and linearization.
- Systems of equations.
- Hamiltonian and gradient systems.
- Rudiments of global theory.
- Numerical methods for ODEs
Research Description for 2007.
The research problems to be considered will be related to the following topics:
- More accurate algorithms in numerical linear algebra.
- Motion of point vortices and filaments.
- Vortex sheet dynamics.
- Discretization of singular
integrals.
Faculty in the program