Part IB
Polynomial interpolation
Orthogonal polynomials
Approximating linear functionals
Gaussian quadrature
The Peano Kernel Theorem
ODEs
Linear stability
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
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
Linear Algebra