Mathematical Modelling - Block 6 (Mathematical Methods and Models: Block 6)

This block contains units 21 - 24 Unit 21 Fourier Series; This 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 Equations; This 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 Fields; The 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 Calculus; This 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.