By the end of the course students will be able to demonstrate a knowledge and broad understanding of Mathematical Methods. They should be able to describe and analyse quantitatively processes, relationships and techniques relevant to the topics included in the course outline, applying these ideas and techniques to solve general classes of problems which may include straightforward unseen elements. They should be able to write down and, where appropriate, either prove or explain the underlying basis of physical laws relevant to the course topics, discussing their applications and appreciating their relation to the topics of other courses taken.