BEng Civil Engineering

The course unit aims to provide a basic course in calculus and algebra to students with A-level mathematics or equivalent.

Apply standard calculus rules and methods to compute derivatives and integrals of functions of one variable, and partial derivatives of functions of two variables.

Apply arithmetical operations to complex numbers in standard and exponential form, analyse complex numbers on the Argand diagram, and interpret sinusoidal functions using phasors.

Compute line integrals and double integrals in two dimensions using Cartesian and polar coordinates, and apply Green’s theorem to evaluate line integrals or double integrals over planar regions.

Express piecewise functions using Macaulay bracket notation and interpret them graphically.

Apply the trapezium rule and Simpson's rule to approximate definite integrals numerically, and apply the bisection method and the Newton-Raphson method to approximate solutions of algebraic  equations.

Solve first-order ordinary differential equations and initial value problems using standard analytical methods.

Understand fundamental concepts of probability theory, including conditional probability.

Use vector operations to formulate and solve geometry problems involving lines and planes.

 

Intermediate calculus. 
Review of product, quotient and chain rules for differentiation. Partial differentiation in two variables. Review of methods of integration (by parts, substitution, and partial fractions). Macaulay brackets.

Double integrals and line integrals. 
Double integrals over rectangles and disks. Line integrals and integrals with respect to arc-length. Relation through Green's theorem.

Basic numerical methods. 
Trapezium rule and Simpson's rule, inc. estimation of error. Bisection method and Newton-Raphson method for solving nonlinear equations.

Vectors. 
Review of vectors in component form; vector addition, parallelogram and triangle of vectors. Vector equation of a straight line. Scalar and vector products. Triple Products. Applications including vector products and areas.

Complex numbers. 
Definition, algebraic operations, modulus and argument. Argand diagram, De Moivre's theorem. Phasors.

Ordinary differential equations (ODEs). 
Examples of first and second-order ODEs. Role of arbitrary constants. 
Solution of first-order separable, linear. and exact ODEs. First-order linear ODEs and integrating factors.

Probability. 
Deterministic vs random (probabilistic) models. Random experiments and sample spaces. Definition and properties of probability; finite sample spaces. Conditional probability, independent events. 

Coursework 1; Weighting within unit 10%; ILOs:

Calculus

Vectors and Geometry

 

Coursework 2; Weighting within unit 10%; ILOs:

Calculus

Complex numbers

Line integrals and multiple integrals 

 

Examination; Weighting within unit 80%; ILOs:

Calculus

Complex numbers

Line integrals and multiple integrals

Macaulay brackets

Numerical methods

Ordinary differential equations

Probability

Vectors and Geometry 

Stroud, K. A. (2013). Engineering mathematics. Palgrave Macmillan. ISBN: 1137031220

Stroud, K. A. (2020). Engineering Mathematics. Bloomsbury Publishing Plc. ISBN: 9781352010282

Kreyszig, E. (2006). Advanced engineering mathematics. Wiley. ISBN: 9780471728979 

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 further information about scholarships and bursaries, please see our undergraduate fees pages or visitour scholarships and bursaries page.