2020-2학기 필답시험(전공종합시험)이 다음과 같이 있을 예정이오니 응시학생께서는 참고하시기 바랍니다.
필답시험일: 2021.02.04(목) 오전10시~오후12시 (2시간)
가이드라인: 2021.01.18일 공지 예정
시험장소: 첨단관6층 (당일 공지 예정/방역수칙 준수/오프라인시험 실시)
[NPDE Guidelines]
For the Numerical PDE qualifying exam, the following materials will be included, but not limited to.
Also in-class exams can be helpful.
1. . Finite difference methods
- Stability of time stepping
- Stability region in the complex plane
- Runge-Kutta methods
- Crank-Nicolson method
- Stability/consistency and difference formula
- Upwind scheme
- Role of advection vs diffusion in terms of stability
- Concept of inflow/outflow
2. Finite volume methods
- Basic concept
- FVM for advection equations
3. Finite element methods
- Basic concept
- Basic formulation for 1D Poisson
4. FDM vs. FVM vs. FEM vs. DG
- Basic concept and Comparison
[NA Guidelines]
For the Numerical Analysis qualifying exam, the following materials will be included, but not limited to.
Also midterm and final exams can be helpful.
1. Rootfinding
- Bisection, Newton, Secant
- Fixed point iteration
2. Interpolation
- Lagrange, Newton, Hermite
- Splines
3. Approximation of functions
- Least squares for discrete data
- Orthogonal polynomials
- Least Squares Approximation Problem
4. Numerical integration
- Trapezoidal, Simpson
- Gauss quadrature
5. Numerical ODE
- unique solvability
- Euler, Crank-Nicolson, Runge-Kutta
- Stability, Root condition
6. Linear algebra
- LU, SVD
- Condition number
- Jacobi, Gauss-Seidel, SOR
- Minimization Algorithm: Gradient method, CG