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Exponential functions and Napierian logarithms; complex numbers - Cartesian complex numbers, the Argand diagram, De Moivre's theorem; polar co-ordinates; partial fractions; the binomial theorem - Pascal's triangle; arithmetical and geometric progressions; the theory of matrices and determinants; the solution of simultaneous equations by matrices and determinants; the solution of triangles and their areas; the solution of three-dimensional triangulation problems; graphs of sine and cosine functions; combining periodic waveforms; compound angles; vectors, vector addition and subtraction and vector products; differentiation from first principles; methods of differentiation; applications of differentiation; introduction to integration; integration using substitutions and partial fractions; integration by parts; numerical integration - Simpson's rule; areas under and between curves; mean and root mean square values; volumes of solids of revolution; centroids of simple shapes - theorem of Pappus; second moments of areas of regular sections; introduction to differential equations; solution of first order differential equations by separation of variables.