MATHEMATICS 2 - 2026/7

Module Overview

Mathematics is an essential tool to understand and solve real-world engineering problems. This module builds on the mathematical foundations from MAT1044 Engineering Mathematics to introduce and explore more advanced mathematical concepts and methods relevant to a wide range of engineering applications. 

Module provider

Sustainability, Civil & Env Engineering

Module Leader

DOHERTY Daniel (Maths & Phys)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 4

Module cap (Maximum number of students): N/A

Module Availability

Semester 2

Prerequisites / Co-requisites

None

Module content

Indicative content includes: 

• Ordinary Differential Equations (ODEs):

Core topics: separable first order linear ODEs and changes of variables; first order linear ODEs using the integrating factor method; first and second order linear ODEs with constant coefficients including homogeneous and non-homogeneous ODEs with exponential, trigonometric and polynomial driving functions; initial value problems and boundary value problems arising in engineering. 

• Matrices and Eigenvalue Problems:       

Core topics: matrices; matrix addition; multiplication by a scalar; matrix multiplication; matrix determinants for 2x2 and 3x3 matrices; transpose matrix; inverse matrix for 2x2 and 3x3 matrices; rank of a matrix; solving systems of linear equations using matrices and Gaussian elimination; Cramer¿s rule; eigenvalues and eigenvectors; examples of eigenvalue problems arising in engineering. 

• Probability and Statistics:       

Revision topics: descriptive statistics including numerical (mean, mode, median and variance) and graphical summaries.Core topics: elementary laws of probability; mutually exclusive events; independent events; discrete probability distributions (random variable, pmf, mean and variance); examples including the binomial and Poisson distributions; continuous probability distributions (random variable, pdf and cdf, mean and variance); examples including the normal distribution; applications in engineering contexts.Extension topics: Statistics with MatLab; the method of least squares to fit straight lines and simple curves (e.g. parabolae) to data. 

• Fourier Series:       

Core topics: Fourier series in real trigonometric form; orthogonality relations for cosine and sine functions; calculating real Fourier series of periodic functions; Fourier series in complex exponential form; orthogonality relations for exponential functions; calculating complex Fourier series of periodic functions; applications in engineering contexts. 

• Introduction to Fourier Transforms and Laplace Transforms: 

Core topics: Fourier transform and inverse Fourier transform (definition and basic properties); calculating Fourier and inverse Fourier transforms; table of Fourier transforms; Laplace transform (definition and properties); calculating Laplace transforms; table of Laplace transforms; inverse Laplace transform using tables; applications of Laplace transforms to initial value problems in engineering contexts. 

• Partial Differential Equations (PDEs): 

Core topics: introduction to linear PDEs; method of separation of variables; examples including the heat equation and wave equation.  

Assessment pattern

Alternative Assessment

N/A

Assessment Strategy

The assessment strategy is designed to to provide students with the opportunity to demonstrate:

• Knowledge and understanding of mathematical concepts and rules.
• The ability to identify and use the appropriate techniques to solve mathematical and engineering problems.

Thus, the summative assessment consists of:

• One in-semester test (50 minutes), run online in an invigilated computer laboratory, worth 20% of the module mark, corresponding to Learning Outcomes 1 to 4.
• A synoptic examination (2 hours), worth 80% of the module mark, corresponding to all Learning Outcomes 1 to 7.

Formative assessment There are regular formative online unassessed courseworks over an eleven week period, designed to consolidate student learning.  FeedbackStudents will receive feedback on the online unassessed courseworks and online in-semester test. This feedback is timed so as to assist students with preparation for the final synoptic examination. Students will also receive verbal feedback at the weekly tutorials, which are designed to promote student engagement with mathematical and engineering problems.

Module aims

• Extend students' understanding of mathematical concepts and techniques.
• Provide students with an introduction to ordinary differential equations, matrices and eigenvalue problems, probability and statistics, Fourier series, Fourier and Laplace transforms, and partial differential equations.
• Enable students to apply their mathematical knowledge and skills to engineering problems.

Learning outcomes

Methods of Teaching / Learning

   The learning and teaching strategy is designed to:

• Provide students with revision of A-level material on statistics.
• Provide students with an understanding of ordinary differential equations, matrices and eigenvalue problems, probability and statistics, Fourier series, Fourier and Laplace transforms, and partial differential equations, supported by extensive use of examples and applications.
• Provide students with experience of mathematical methods used to understand and solve engineering problems.

 The learning and teaching methods include:

• Three one-hour lectures for eleven weeks, with module notes provided to complement the lectures. These lectures provide a structured learning environment and opportunities for students to ask questions and to practice methods taught.
• Eleven tutorials for guided discussion of solutions to problem sheets (provided to students in advance) to reinforce their understanding of mathematical concepts and methods, and enable students to engage in solving mathematical problems relating to engineering sciences.
• Formative online unassessed courseworks designed to provide students with opportunities to consolidate learning. Feedback on these unassessed courseworks will provide students with guidance on their progress and understanding.
• Lectures will cover core topics. Video recordings of core topics covered in lectures may be provided. These recordings are intended to give students an opportunity to review parts of lectures which they may not fully have understood and should not be seen as an alternative to attending lectures.
• Additional video recordings of revision topics and extension topics will be provided. Extension topics will also be covered via problems discussed in tutorials using a flipped learning approach.

   

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Reading list

https://readinglists.surrey.ac.uk
Upon accessing the reading list, please search for the module using the module code: ENG1085

Other information

The Faculty of Engineering and Physical Sciences is committed to developing graduates with strengths in Digital Capabilities, Employability, Global and Cultural Capabilities, Resourceness and Resilience, and Sustainability. This module is designed to allow students to develop knowledge, skills and capabilities in the following areas:   Digital Capabilities: The SurreyLearn page for ENG1085 features a dynamic discussion forum where students can pose questions and engage with others using e.g. LaTeX and MathML tools. This enhances their digital competencies while facilitating collaborative learning and information sharing. Students also complete digital assessments which enable them to further develop their digital capabilities. Employability: The module ENG1085 equips students with skills which significantly enhance their employability. The mathematical proficiency gained hones critical thinking and problem-solving abilities. Students learn to analyse real-world problems and apply mathematical techniques to arrive at solutions. These are highly sought after skills in engineering and in many professions. Global and Cultural Capabilities: Students enrolled in ENG1085 originate from a variety of countries and have a wide range of cultural backgrounds. Students are encouraged to work together during problem-solving teaching activities in tutorials and lectures, which naturally facilitates the sharing of different cultures. Resourcefulness and Resilience: ENG1085 is a module which demands the analytical ability to perform mathematical calculations accurately. Students will gain skills in mathematically modelling engineering problems, and will complete assessments which challenge them and build resilience.

Programmes this module appears in

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2026/7 academic year.