Ordinary differential equations of the first order -- Linear differential equations with constant coefficients -- Simultaneous linear differential equations -- Finite differences -- Mechanical and electric circuits -- Fourier series and integrals -- The Laplace transformation -- Partial differential equations -- Bessel functions and legendre polynomials -- Determinants and matrices -- Further properties of matrices -- The calculus of variations -- Vector analysis -- Tensor analysis -- Analytic functions of a complex variable -- Infinite series in the complex plane -- The theory of residues -- Conformal mapping