Standard syllabus
Numerical analysis · Graduate · Math
Topics
Approximation and stability theory
- Best approximation in normed spaces (introduction)
- Polynomial and spline approximation theory
- Stability, consistency, and convergence for numerical methods
- A-stability and stiff ODEs
- Conditioning of linear and nonlinear problems
Linear and nonlinear systems
- Direct methods: LU, Cholesky, and QR factorizations
- Iterative methods: Krylov subspaces and GMRES (introduction)
- Preconditioning strategies
- Newton–Kantorovich convergence analysis (introduction)
- Eigenvalue algorithms: QR iteration and Lanczos method
Numerical PDEs (introduction)
- Finite difference methods for elliptic, parabolic, and hyperbolic PDEs
- Consistency, stability, and convergence (Lax equivalence overview)
- Finite element method: Galerkin formulation (introduction)
- Multigrid methods (conceptual overview)
- Adaptive mesh refinement (introduction)
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$1,162 · Numerical analysis · 18 tutoring hrs
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