Department of MathematicsThis is a Qualifying Eligible (QE) course for the Math PhD with regular, graded HW and a comprehensive final exam.
Prerequisites
A solid grasp of undergraduate multivariable calculus, linear algebra and differential equations is essential. Experience with programming of some kind is also expected (be comfortable with writing code to implement algorithms).
Syllabus
Approximation using polynomials, splines, Fourier series. Least square approximation. Numerical differentiation and integration. Ordinary differential equations: initial value and boundary value problems, explicit and implicit methods, stiffness, stability and convergence. Partial differential equations: introduction to finite difference methods, spectral methods, finite element (Galerkin) methods.
References
- Numerical Mathematics (2nd edition), Quarteroni, Sacco, Saleri.
- Numerical Analysis: Mathematics of Scientific Computing, Kincaid, Cheney and Cheney.