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Topics: Revision of old exams, see Final Examination Info; questions

Check list lecture 18 - 24:

- Eigenvalue
- Eigenvalue problem
- What is an eigenvalue and eigenvector
- Calculating (with) eigenvalues and eigenvectors
- Rayleigh quotient
- Power Method (how/why does it work, convergence, ... )
- Shifted Inverse Power Method (how/why does it work, convergence, ... )
- Similar matrices
- QR method for eigenvalue problem

- Singular value decomposition (SVD)
- what is it?
- how can it be computed?
- properties of the SVD
- relation between singular values and original matrix
- low-rank approximation (Example: compression)

- Numerical Differentiation
- forward/backward/centered difference formula
- difference formula for higher derivates
- Computing the order of a difference formula
- Deriving difference formula
- error analysis
- numerical differentiation in matrix form

- Numerical Integration (quadrature)
- Newton-Cotes formulas (open and closed, Trapezoid(al) rule, Simpson rule, midpoint rule)
- properties of Newton-Cotes formulas
- Exactness of a quadrature
- Error formula
- Computation of weights
- Transformation of nodes and weights (change of interval)
- Composite quadrature
- Adaptive quadrature
- Maximal exactness of quadratures
- Gauss-Legendre quadrature (properties)

- Fourier Transformation
- Discrete Fourier transformation
- Fast Fourier transformation