Notes — Units III and IV (Differential Equations), with part of I and II
Covers Units III and IV of AR104 in full. Unit III, ordinary differential equations: separable and exact equations, integrating factors, Bernoulli equations, homogeneous linear equations of second and higher order with constant coefficients, Euler-Cauchy equations, the Wronskian, undetermined coefficients and variation of parameters. Unit IV, partial differential equations: the heat, wave and Laplace equations solved by separation of variables, with Fourier series worked alongside. Units I and II, linear algebra, are only PARTLY covered — matrix types, rank, systems of linear equations, eigenvalues, eigenvectors and diagonalisation are here, but vector spaces, subspaces, basis and dimension, the rank-nullity theorem, LU decomposition, singular value decomposition and quadratic forms are not.