BEng/MEng Mechanical Engineering with an Integrated Foundation Year

The course unit aims to provide a second semester course in calculus and algebra to students in Foundation Studies entering University with AS-level mathematics or equivalent.

On completion of this unit, successful students will be able to

1) Carry out arithmetic operations (including the finding of roots) on complex numbers and represent the results in cartesian, polar and exponential forms as well as on an Argand Diagram.

2) Solve and analyse systems of linear equations using matrices.

3) Calculate improper integrals and analyse functions that are defined by integrals.

4) Solve homogeneous, separable and linear first-order Ordinary Differential Equations and analyse their properties using direction fields.

5) Carry out partial differentiation and use the chain rule to estimate errors in functions.

Complex Numbers (4 lectures) :

• Definition.
• Arithmetic operations in Cartesian form.
• Argand Diagram.
• Modulus, argument and conjugate.
• Polar and Exponential forms.
• Roots of complex numbers.

Matrices (6 lectures)

• Definition
• Addition, subtraction and multiplication by a scalar
• Multiplication of two matrices
• Square matrices
• Solution of equations
• Inverse Matrices
• Determinants

Further Integration (3 lectures)

• Improper integrals
• Functions defined by integrals (error function etc)

Ordinary Differential Equations (5 lectures)

• First-order differential equations.
• General and particular solutions
• Direction fields and qualitative solutions
• Separable equations
• Linear equations and the integrating factor
• Homogeneous equations

Partial Differentiation (4 lectures)

• Definition of partial differentiation
• The chain rule for differentiation
• Total Derivatives

Using partial differentiation to estimate errors

Coursework 1 (week 4). Weighting within unit 10%

Coursework 2 (week 10). Weighting within unit 10%

Examination in semester 2. Weighting within unit 80%

BOSTOCK, L., & CHANDLER, S. 1981. Mathematics - the core course for A-level. Thornes, Cheltenham. (ISBN0859503062)

BOSTOCK, L., CHANDLER, S., & ROURKE, C. 1982. Further pure mathematics. Thornes, Cheltenham. (ISBN0859501035)

CROFT, T. & DAVISON, R, 2008. Mathematics for engineers: a modern interactive approach (3rd ed.) Pearson, Harlow.

This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  

Please see Blackboard / course unit related emails for any further updates

Tuition fees for home students will be £10,050 for the 2027/28 academic year. In England and Wales, tuition fees for home undergraduate students are subject to the Government fee cap, which the Government has announced will be £10,050 for the 2027/28 academic year.

Government policy is to increase the fee cap on an annual basis to reflect inflation (i.e. increasing costs), and the tuition fee home students pay in subsequent academic years will reflect any increases in the Government fee cap (which we will communicate to you as soon as we can in advance of the relevant academic year).

Tuition fees for international students will be £29,200 for the 2027/28 academic year. For subsequent academic years, the University reserves the right to increase the tuition fee by up to 7% each year, including to reflect rising costs associated with delivering our education and wider student experience.

For general information please see the undergraduate finance pages.

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

The Foundation Year Bursary  is available to UK students who are registered on an undergraduate foundation year here and who has had a full financial assessment carried out by Student Finance.

Details of country-specific funding available to international students can be found within our  International country profiles .

The University of Manchester is committed to attracting and supporting the very best students. We have a focus on nurturing talent and ability, therefore, we want to make sure that you have the opportunity to study here, regardless of your financial circumstances.

For information about scholarships please visit our  undergraduate student finance pages  and the Department funding pages that you intend to progress to after successfully completing the Foundation Year.