Part IB
Polynomial interpolation Orthogonal polynomials Approximating linear functionals Gaussian Quadrature The Peano Kernel Theorem Numerical Methods for Ordinary Differential Equations Linear stability Numerical Linear Algebra
Part II
Lecture slides on link: https://www.damtp.cam.ac.uk/research/afha/lectures/Part_II_NumAn/
Poisson Equation Discrete Fourier Transform (Sequences)
Stability of Numerical Methods Consistency of Numerical Methods Lax Equivalence Theorem Diffusion Equation Advection Equation
Fourier Analysis of Stability Unbounded Diffusion Equation Unbounded Advection Equation Unbounded Wave Equation
Numerical Schemes as Approximations to Exp Splitting Numerical Schemes 2D Diffusion Equation
Spectral Numerical Methods Fourier Approximation of Functions Chebyshev Polynomials Numerical Linear Algebra