MEng Civil Engineering

To provide a second-semester course in calculus and algebra to students with A-level mathematics or equivalent.

Using conditions where appropriate, solve certain second-order Ordinary Differential Equations and simple partial differential equations (or verify potential solutions provided) and interpret the solutions  

Use L'Hopital's rule and other rules to calculate limits  

Use rules to determine whether a series is convergent or divergent or to find the radius of convergence.  

Express a function around a given point (in one or two dimensions) as a Taylor or Maclaurin series and use the series to estimate the function; acknowledge the limitations of the series approach.  

Calculate total derivatives and convert partial derivatives between appropriate coordinate systems  

Locate and classify stationary points of functions of two variables  

Carry out arithmetic operations on matrices and calculate determinants and inverse matrices  

Apply matrix and other techniques (e.g. Gaussian Elimination) to solve systems of linear algebraic equation and interpret the results.  

 

Second-order Ordinary Differential Equations. Linear Equations with constant coefficients; homogeneous and non-homogeneous cases; complementary functions and particular integrals, Special cases with non-constant coefficients.

Series and Limits. Definition of Limits. L'Hopital's Rule. Sequences and Series; convergence; Power Series, Taylor and Maclaurin Series.

Partial Differentiation. Chain rule for partial differentiation. Total derivatives. Theory of errors. Coordinate Systems (Cartesian, Cylindrical, Spherical), change of variables.

Functions of Two Variables. Maxima, minima and saddle points. Taylor Series in two variables.

Partial differential equations (wave, heat/diffusion, Laplace/Poisson. Solution by separation of variables.

Matrices and Determinants: Definition of an m x n matrix. Matrix addition, subtraction, multiplication by a scalar, matrix multiplication; square matrices, determinants and properties; Solution of equations; inverse matrices.

Linear Algebra: Solution of simultaneous equations; Gaussian elimination. 

Coursework 1; Weighting within unit 10%; ILOs:

Solve ODEs

 

Coursework 2; Weighting within unit 10%; ILOs:

Calculate Limits

Determine Series convergence

Express a function as a series

Calculate total derivatives etc. 

 

Exam; Weighting within unit 80%; ILOs:

Solve ODEs and PDEs

Calculate Limits

Determine Series convergence

Express a function as a series

Calculate total derivatives etc.

Locate/classify stationary points

Arithmetic Operations on Matrices

Solve systems of algebraic equations

K A Stroud, Engineering Mathematics, Palgrave Macmillan

HELM, Helping Engineers Learn Mathematics, online

AC Croft et. al. Mathematics for Engineers. Pearson Education

K A Stroud, Advanced Engineering Mathematics, Palgrave Macmillan 

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 commencing their studies in September 2027 will be £10,050 per annum. Tuition fees for international students will be £37,500 per annum.

For general information please see the undergraduate finance pages.

There is acompulsory field course for Civil Engineering students which incurs a subsidised fee* (approx. £100) that contributes to travel, accommodation, and subsistence. You are expected to bring your own wet weather clothing and footwear.

The exact cost and dates of the trip are confirmed at the start of your second year.

*In accordance with current university policy, this fee is restricted to be not more than 1% of the annual tuition fee of the course.

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

For information about fees and funding, please see our undergraduate fees pages and check the scholarships and bursaries page.