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Programme & Unit Catalogues

## AR20386: Mathematics 2

Owning Department/School: Department of Architecture & Civil Engineering
Credits: 6
Level: Intermediate (FHEQ level 5)
Period: Semester 1
Assessment: EX 100%
Supplementary Assessment: Like-for-like reassessment (where allowed by programme regulations)
Requisites:
Description: Aims:
To provide a general mathematical basis for the development of engineering subjects at second year level of the civil engineering programmes, and preparation for year 3 work.

Learning Outcomes:
On successful completion of the unit, the student will be able to demonstrate an understanding and ability to use the following techniques, as detailed in the 'Contents':
* Ordinary Differential equations;
* Functions of several variables;
* Numerical Methods.

Skills:
An understanding of the mathematical tools used in engineering analysis and how they can be applied to civil engineering problems.

Content:
Ordinary Differential equations Simple first order using separation of variables and integrating factor. Linear equations with constant coefficients using trial method for particular integral. Simultaneous equations. Application of differential equations to mechanical systems and structural problems. Functions of several variables: Multiple Integration, Partial differentiation. Separation of variables, Laplace's equation, diffusion and wave equations. Fourier series Full and half-range series. Odd and even functions, odd harmonics. Numerical Methods: Method of least squares, Finite differences, interpolation using Lagrange and Newton difference formulae. Error estimation, splines, Numerical solution of ordinary differential equations. Euler, improved Euler, Runge-Kutta methods. Accuracy and stability. Initial and boundary value problems. Numerical integration. Root finding Newton Raphson, Secant method. Use of computers in solving engineering mathematics problems.
Programme availability:

#### AR20386 is Compulsory on the following programmes:

Department of Architecture & Civil Engineering
• UEAR-AFB07 : BEng (hons) Civil Engineering (Full-time) - Year 2
• UEAR-AKB07 : BEng (hons) Civil Engineering (Full-time with Thick Sandwich Placement) - Year 2
• UEAR-AFM03 : MEng (hons) Civil and Architectural Engineering (Full-time) - Year 2
• UEAR-AKM03 : MEng (hons) Civil and Architectural Engineering (Full-time with Thick Sandwich Placement) - Year 2
• UEAR-AFM07 : MEng (hons) Civil Engineering (Full-time) - Year 2
• UEAR-AKM07 : MEng (hons) Civil Engineering (Full-time with Thick Sandwich Placement) - Year 2

Notes:
* This unit catalogue is applicable for the 2012/13 academic year only. Students continuing their studies into 2013/14 and beyond should not assume that this unit will be available in future years in the format displayed here for 2012/13.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.