Linear Algebra II - M&P, M&CS
This course is an introduction to determinants, linear transformations, eigenvectors and eigenvalues and the spectral theorem for real symmetric matrices. It covers both theory and applications of diagonalizability amd brings in the geometrical importance of an orthogonal change of variable.
Groups and Group Actions - M&P, M&CS
Abstract algebra evolved in the twentieth century out of nineteenth century discoveries in algebra, number theory and geometry. The group is an important first example of an abstract, algebraic structure and groups permeate much of mathematics particularly where there is an aspect of symmetry involved.
Analysis II: Continuity and Differentiability - M&P, M&CS
In this term’s lectures, we study the continuity of functions of a real or complex variable, and differentiability of functions of a real variable.
The subject of dynamics is about how things change with time. A major theme is the modelling of a physical system by differential equations, and one of the highlights involves using the law of gravitation to account for the motion of planets.
In these lectures, students will be introduced to multi-dimensional vector calculus. They will be shown how to evaluate volume, surface and line integrals in three dimensions and how they are related via the Divergence Theorem and Stokes’ Theorem.
Fourier Series and PDEs
Fourier series are a way of representing functions as sums of trigonometric functions. Students will then be shown how the heat equation, the wave equation and Laplace’s equation arise in physical models.
In this term you undertake an assessed project using MATLAB and there are drop-in sessions and demonstration sessions.