NATS1185 Further Mathematics for Scientists

10 creditsClass Size: 100

Module manager: Marcelo P de Miranda
Email: m.miranda@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2024/25

Pre-requisite qualifications

Grade B or above in A level Mathematics (or equivalent)

Module replaces

NATS2380

This module is not approved as a discovery module

Module summary

Mathematical knowledge and skills are essential for the successful training of scientists and important for the professional life of scientists. This module will be taken by science students who have grade B or above in A’level mathematics (or equivalent); its aim will be to enable students to gain competence in areas of mathematics that are particularly relevant for scientists but are not part of the A level syllabus.

Objectives

On completion of this module, students should have extended their range of mathematical skills and techniques to include a set of specialised mathematical manipulations appropriate to the study of science and be able to apply these to scientific problems.

The topics of study will be discussed in lectures and extensively practiced via problem solving in workshops.

Learning outcomes
On successful completion of the module students will have demonstrated the following learning outcomes:

1. Use partial derivatives to extend the applications of differentiation of functions of a single variable to differentiation of functions of two or more variables.
2. Find general and particular solutions of basic ordinary differential equations.
3. Use complex numbers in arithmetical and algebraic operations, including the solution of polynomial equations, evaluation of functions of complex variables, and graphical representations of complex numbers.
4. Perform mathematical operations on or using the most widely-used types of matrices, including the solution of systems of coupled linear equations and the transformation of coordinates.

Skills Learning Outcomes

On successful completion of the module students will have demonstrated the following skills:

a) Core Literacies: Display mathematical skills and apply mathematics in the context of everyday situations.
b) Problem solving & analytical skills

Syllabus

Review of introductory differential calculus (first and higher derivatives of functions of a single variable; product, quotient, and chain rules for differentiation; location of extrema) and integral calculus (indefinite and definite integration of functions of a single variable, including integration by substitution or by parts).

Partial differentiation and full differentials of functions of two or more variables.

Differential equations, boundary or initial value problems, eigenvalue problems. Their relevance, and solution of simple cases.

Addition, subtraction and multiplication with matrices. Basic types of matrices. Matrix determinants and inversion. Linear algebraic solution of simultaneous linear equations. Matrices as linear transformation operators.

Methods of Assessment

We are currently refreshing our modules to make sure students have the best possible experience. Full assessment details for this module are not available before the start of the academic year, at which time details of the assessment(s) will be provided.

Assessment for this module will consist of;

1 x In-person open-note exam

Teaching methods

 Delivery type Number Length hours Student hours Workshop 11 1.00 11.00 Lectures 11 1.00 11.00 Independent online learning hours 12.00 Private study hours 66.00 Total Contact hours 22.00 Total hours (100hr per 10 credits) 100.00

Opportunities for Formative Feedback

Workshops (problem solving, face-to-face, weekly during teaching weeks, 1 hour)