Mathematical Modelling - Block 3 (Mathematical Methods and Models: Block 3)

This block contains units 9-12 Unit 9 Matrices and Determinants; This unit examines some of the properties and applications of matrices. It introduces the matrix method of solving large systems of linear equations, called the Gaussian elimination method, and explains the conditions required for this method to work. Unit 10 Eigenvalues and Eigenvectors; This unit introduces eigenvectors showing simplified problems. It considers the eigenvectors and eigenvalues associated with various linear transformations of the plane and outlines situations where eigenvectors and eigenvalues are useful. Unit 11 Systems of Differential Equations; This unit focuses on systems of linear differential equations relating two more functions and their derivatives. It shows how various situations can be modelled by a system of linear differential equations, how such a system can be written in matrix form, and how eigenvalues and eigenvectors can be used to solve it when the equations are homogeneous with constant coefficients. Unit 12 Functions of Several Variables; This unit extends the calculus of functions of one variable to functions of several variables. It also discusses the application of functions of several variables to mechanics.