# 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)

### Contact hours and workload

This module is approximately 150 hours of work. This breaks down into about 42 hours of contact time and about 108 hours of independent study. The University may make minor variations to the contact hours for operational reasons, including timetabling requirements.

We regularly review our modules to incorporate student feedback, staff expertise, as well as the latest research and teaching methodology. We’re planning to run these modules in the academic year 2023/24. However, there may be changes to these modules in response to COVID-19, staff availability, student demand or updates to our curriculum. We’ll make sure to let our applicants know of material changes to modules at the earliest opportunity.

### Courses

This module is offered on the following courses: