Many mathematical problems, e.g. diferential equations, can be solved generally only by computation, using discretisation methods. In other cases, e.g. large systems of linear equations, calculation of the exact solution is impractical and, again, we need to resort to numerical methods. Numerical analysis concerns itself with the design, implementation and mathematical understanding of computational algorithms. The course will address iterative techniques for linear equations, the calculation of eigenvalues and eigenvectors, and the solution of partial diferential equations by finite differences (following the treatment of ordinary diferential equations in Part IB). The last section of the course deals with Fourier expansions and their generalisations.
The concept of converting a grid to a column vector using the 'natural ordering' (ordering by columns) is quite simple, but is best explained using an animation. If you didn't understand this concept (discussed in the first few lectures), then this video is for you!