#### Prerequisites
* A level Mathematics at Grade A or better, or equivalent.
#### Corequisites
* Single Mathematics A (MATH1561).
#### Excluded Combination of Modules
* Mathematics for Engineers and Scientists (MATH1551) may not be taken with or after this module.
#### Aims
* This module has been designed to supply mathematics relevant to students of the physical sciences.
#### Content
* Vectors: including scalar and vector products, derivatives with respect to scalars, two-dimensional polar coordinates.
* Ordinary differential equations: including first order, second order linear equations, complementary functions and particular integrals, simultaneous linear equations, applications.
* Fourier analysis: including periodic functions, odd and even functions, complex form.
* Functions of several variables: including elementary vector algebra (bases, components, scalar and vector products, lines and planes), partial differentiation, composite functions, change of variables, chain rule, Taylor expansions. Introductory complex analysis and vector calculus
* Multiple integration: including double and triple integrals.
* Introduction to probability: including sample space, events, conditional probability, Bayes' theorem, independent events, random variables, probability distributions, expectation and variance.
#### Learning Outcomes
Subject-specific Knowledge:
* By the end of the module students will: be able to solve a range of predictable or less predictable problems in Mathematics.
* have an awareness of the basic concepts of theoretical mathematics in these areas.
* have a broad knowledge and basic understanding of these subjects demonstrated through one or more of the following topic areas: Vectors.
* Ordinary differential equations.
* Fourier analysis.
* Partial differentiation, multiple integrals.
* Vector calculus.
* Probability.
Subject-specific Skills:
Key Skills:
#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module
* Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
* Initial diagnostic testing fills in gaps related to the wide variety of syllabuses available at Mathematics A-level.
* Tutorials provide the practice and support in applying the methods to relevant situations as well as active engagement and feedback to the learning process.
* Weekly coursework provides an opportunity for students to consolidate the learning of material as the module progresses (there are no higher level modules in the department of Mathematical Sciences which build on this module). It serves as a guide in the correct development of students' knowledge and skills, as well as an aid in developing their awareness of standards required.
* The end-of-year written examination provides a substantial complementary assessment of the achievement of the student.
