ENGINEERING MATHEMATICS - 2026/7

Module Overview

Mathematics is the best tool we have to gain a quantitative understanding of engineering sciences. This module is designed briefly to revise and then to extend A-level Mathematics material, and to introduce students to mathematical techniques to support future engineering modules.

Module provider

Mathematics & Physics

Module Leader

PRINSLOO Andrea (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 1

Prerequisites / Co-requisites

None

Module content

Indicative content includes: 

• Algebra: Revision topics: basic algebra, quadratic formula and factorisation of polynomials; factorials, permutations and combinations; Pascal's triangle and binomial theorem; simultaneous equations; partial fractions. 
• Vectors: Core topics: vectors as quantities with magnitude and direction; graphical representations of vectors; resolution of a vector into components; magnitude of a vector; vector addition and subtraction; multiplication of a vector by a scalar; unit vectors; dot product; cross product. 
• Functions: Revision topics: trigonometric functions and graphs; trigonometric identities. Core topics: concept of a function and inverse function; composite functions; odd and even functions; periodic functions; exponential functions and exponential laws; hyperbolic functions; logarithmic functions and laws of logarithms; limits and continuity. Extension topics: inverse trigonometric functions; solving trigonometric equations. 
• Differentiation and Series: Revision topics: sigma notation; arithmetic and geometric series. Core topics: Gradients of curves and definition of the derivative; tangent lines; standard derivatives and rules of differentiation; higher derivatives; implicit, logarithmic and parametric differentiation; local extrema and curve sketching; power series; McLaurin and Taylor series expansions; examples of series expansions (cosine, sine, exponential and natural logarithm); binomial series; evaluation of limits and l'Hôpital's rule. Extension topics: Newton-Raphson method; differentiation of vector functions of a single variable; applications to classical mechanics. 
• Complex Numbers: Core topics: definition of a complex number; real and imaginary parts; algebra of complex numbers; Argand diagram; cartesian and polar forms of complex numbers; definition of the complex exponential as a series expansion; exponential form of complex numbers; complex trigonometric and hyperbolic functions; de Moivre;s theorem and applications. Extension topic: nth roots of complex numbers. 
• Integration: Core topics: anti-derivatives and indefinite integrals; standard indefinite integrals; areas under curves and definite integrals; fundamental theorem of calculus; integration by substitution; integration by parts; integrating rational functions using partial fractions. Extension topics: trigonometric substitution; recurrence relations using integration by parts; applications of integration (mean and root mean square, lengths of curves, surfaces and volumes of revolution, first moments and centroids, second moments and radii of gyration). Partial Differentiation and Double Integration: Core topics: functions of two variables; partial derivatives and higher partial derivatives; gradient and Laplacian; total differentials; local extrema and their classification as local minima, local maxima or saddle points; double integrals with constant and non-constant limits; evaluating double integrals; applications of double integration (areas and centroids). Extension topic: propagation of error.

Assessment pattern

Alternative Assessment

None

Assessment Strategy

The assessment strategy is designed 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 for this module 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 8. 

Formative assessment: There are regular formative online unassessed courseworks over a ten week period, designed to consolidate student learning. Feedback: Students 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

• Consolidate and extend students¿ understanding of basic mathematical concepts and techniques.
• Provide students with an introduction to vectors, functions, differentiation and series, complex numbers, integration, partial differentiation and double integration.
• 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 algebra, functions and series. 
• Provide students with an understanding of vectors, functions, differentiation, series, complex numbers, integration, partial differentiation and double integration, 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 ten 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. 
• Ten 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: MAT1044

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 MAT1044 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 MAT1044 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 MAT1044 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: MAT1044 is a module which demands the analytical ability to perform mathematical calculations accurately. Students will gain skills in analysing mathematical and engineering problems, and will complete assessments which challenge them and build resilience.

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.