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Programme & Unit Catalogues

## AR10367: Mathematics 1

Owning Department/School: Department of Architecture & Civil Engineering
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Certificate (FHEQ level 4)
Period:
Semester 2
Assessment Summary: EX 100%
Assessment Detail:
• Examination (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 first year level of the civil engineering programmes, and preparation for year 2 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: Elementary functions; differentiation and its applications; integration and its applications; determinants and matrices; elementary vector analysis.

Skills:
Ability to manipulate and solve mathematical problems, graphical representation of mathematical functions, development of mathematical ideas relevant to engineering. Visualisation of engineering behaviour in terms of mathematical models, solution of mathematically and statistically described engineering problems. Ability to manipulate geometry and resolve forces in 3D.

Content:
Elementary functions: Exponential and logarithmic functions, hyperbolic functions and inverses in logarithmic form, inverse circular functions, plotting graphs.
Differentiation and its applications: Maximum and minimum values, inflection points, tangents, normals, curvature, solution of non-linear equations using Newton's method, limits.
Integration and its applications: General revision of techniques, by parts, use of partial fractions, substitution, length of curves, areas and volumes, first and second moments, centre of gravity, parallel and perpendicular axes theorem.
Determinants and matrices: Properties of determinants. Matrix algebra. Solution of simultaneous equations using the matrix inverse. Cramer's rule and Gauss elimination. Consistency.
Elementary vector analysis: Basic definitions and algebra. Scalar and vector products. Equations of lines and planes. Geometrical interpretations, orientation of planes, volumes of solids.
Programme availability:

#### AR10367 is Compulsory on the following programmes:

Department of Architecture & Civil Engineering
• UEAR-AFB07 : BEng(Hons) Civil Engineering (Year 1)
• UEAR-AKB07 : BEng(Hons) Civil Engineering with Year long work placement (Year 1)
• UEAR-AFM03 : MEng(Hons) Civil and Architectural Engineering (Year 1)
• UEAR-AKM03 : MEng(Hons) Civil and Architectural Engineering with Year long work placement (Year 1)
• UEAR-AFM07 : MEng(Hons) Civil Engineering (Year 1)
• UEAR-AKM07 : MEng(Hons) Civil Engineering with Year long work placement (Year 1)

 Notes: This unit catalogue is applicable for the 2018/19 academic year only. Students continuing their studies into 2019/20 and beyond should not assume that this unit will be available in future years in the format displayed here for 2018/19. 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. Undergraduates: Find out more about these and other important University terms and conditions here. Postgraduates: Find out more about these and other important University terms and conditions here.