## AR20386: Mathematics 2

[Page last updated: 15 October 2020]

Owning Department/School: Department of Architecture & Civil Engineering
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Intermediate (FHEQ level 5)
Period:
Semester 1
Assessment Summary: CW 10%, EX 90%
Assessment Detail:
• Coursework (CW 10%)
• Examination (EX 90%)
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 (Year 2)
• UEAR-AKB07 : BEng(Hons) Civil Engineering with Year long work placement (Year 2)
• UEAR-AFM03 : MEng(Hons) Civil and Architectural Engineering (Year 2)
• UEAR-AKM03 : MEng(Hons) Civil and Architectural Engineering with Year long work placement (Year 2)
• UEAR-AFM07 : MEng(Hons) Civil Engineering (Year 2)
• UEAR-AKM07 : MEng(Hons) Civil Engineering with Year long work placement (Year 2)

 Notes: This unit catalogue is applicable for the 2020/21 academic year only. Students continuing their studies into 2021/22 and beyond should not assume that this unit will be available in future years in the format displayed here for 2020/21. Programmes and units are subject to change 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.Find out more about these and other important University terms and conditions here.