This block contains units 21 - 24Unit 21 Fourier SeriesThis unit is concerned with the technique of expressing a periodic function as a sum of terms, where each term is a constant, a sine function or a cosine function. This unit assumes you have a background knowledge of the definition of the period (unit 7), forced oscillations and resonance (Unit 17, and integration by parts (Unit 1).Unit 22 Partial Differential EquationsThis unit builds on ideas previously introduced in unit 12 regarding The diffusion equation and the wave equation, in the context of modelling the vibrations of a taut string (such as guitar string).Unit 23 Scalar and Vector FieldsThe main focus of this unit is the differential calculus of scalar and vector fields, i.e. the study of how scalar and vector fields vary from one point to another. A brief introduction to the properties of orthogonal matrices and pictorial representations of scalar and vector fields is given along with an extended discussion of the gradient function of a scalar field. Cylindrical and spherical polar coordinate systems for specifying points in three dimensions is also introduced in this unit.Unit 24 Vector CalculusThis unit discusses the divergence of a vector field, the curl of a vector field, the scalar line integral and linking line integrals curl and gradient. This unit also builds on the concepts of kinetic energy and potential energy.