# Further Mathematics B (G5132)

15 credits, Level 3 (sub-degree)

Spring teaching

This module continues on from Further Maths A and explores:

Exponential functions - one of the most important functions in mathematics, widely used to model change in physical processes, such as change in population size over time.

Planar Graph Theory - we start with the problem of whether it is possible to do a tour of a certain city by crossing all seven bridges once, leading to some simple yet fascinating insights about graphs embedded in a plane.

First and second order differential equations - these equations involve unknown functions and their derivatives. They are used to model many real-world phenomena, and we learn some of the techniques used to solve them.

Integration techniques - we build on previous integration techniques to examine curvature (a measure of how sharply a curve is bending from a tangent line), volume of revolution and surface area of revolution, arc-length, and how to integrate by parts when the formula doesn't lead to a simpler integral.

Vectors, lines and planes - unlike scalars (such as temperature or speed), vectors require in addition a specified direction (such as heat flow or velocity). You will learn methods that have been developed to handle these quantities, leading to vector algebra, vector geometry and vector calculus.

### Teaching 77%: Lecture 23%: Practical (Workshop)

### Assessment 20%: Coursework (Portfolio, Problem set) 80%: Examination (Unseen examination)