## ME10304: Mathematics 1

[Page last updated: 27 October 2020]

Owning Department/School: Department of Mechanical Engineering
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Certificate (FHEQ level 4)
Period:
Semester 1
Assessment Summary: EX 100%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment:
ME10304 Re-Assessment Examination (where allowed by programme regulations)
Requisites: This unit is not normally available to visiting/exchange students.
Description: Aims:
To consolidate and extend topics met at A-level.
To improve students' fluency and understanding of the basic techniques required for engineering analysis.

Learning Outcomes:
After taking this unit the student should be able to:
Handle circular and hyperbolic functions, and sketch curves. Differentiate and integrate elementary functions, products of functions etc.
Use complex numbers.
Employ standard vector and matrix techniques for geometrical purposes. Determine the Fourier series of a periodic function.
Understand power series representations of functions and their convergence properties.

Skills:
Numeracy; working independently.

Content:
Elementary topics: curve sketching; hyperbolic and circular functions; identities; partial fractions; arithmetic and geometric progressions; binomial expansions. Differentiation: limit definition; notation; higher derivatives; standard derivatives; derivative of products and functions of functions; Taylor's series; partial differentiation; critical points. Integration: definition as an area; integration by substitution, using partial fractions; integration by parts; mean and RMS; surfaces and volumes of revolution. Complex numbers: definition; geometric representation; modulus and argument; Cartesian and polar forms; Euler's formula; elementary operations; roots. Vectors and Matrices: definition; unit vectors; classification of matrices; scalar and vector products and their use; geometrical applications; solutions of Ax=b systems; determinants. Fourier Series: definition; interpretation; use of symmetries; convergence properties.
Programme availability:

#### ME10304 is Compulsory on the following programmes:

Department of Mechanical Engineering
• UEME-AFB26 : BEng(Hons) Aerospace Engineering (Year 1)
• UEME-AKB26 : BEng(Hons) Aerospace Engineering with Year long work placement (Year 1)
• UEME-AFB48 : BEng(Hons) Integrated Design Engineering (Year 1)
• UEME-AKB48 : BEng(Hons) Integrated Design Engineering with Year long work placement (Year 1)
• UEME-AFB16 : BEng(Hons) Mechanical Engineering (Year 1)
• UEME-AKB16 : BEng(Hons) Mechanical Engineering with Year long work placement (Year 1)
• UEME-AFB38 : BEng(Hons) Mechanical Engineering with Manufacturing and Management (Year 1)
• UEME-AKB38 : BEng(Hons) Mechanical Engineering with Manufacturing and Management with Year long work placement (Year 1)
• UEME-AFB47 : BEng(Hons) Mechanical with Automotive Engineering (Year 1)
• UEME-AKB47 : BEng(Hons) Mechanical with Automotive Engineering with Year long work placement (Year 1)
• UEME-AFM04 : MEng(Hons) Aerospace Engineering (Year 1)
• UEME-AKM04 : MEng(Hons) Aerospace Engineering with Year long work placement (Year 1)
• UEME-AFM48 : MEng(Hons) Integrated Design Engineering (Year 1)
• UEME-AKM48 : MEng(Hons) Integrated Design Engineering with Year long work placement (Year 1)
• UEME-AFM16 : MEng(Hons) Mechanical Engineering (Year 1)
• UEME-AKM16 : MEng(Hons) Mechanical Engineering with Year long work placement (Year 1)
• UEME-AFM38 : MEng(Hons) Mechanical Engineering with Manufacturing and Management (Year 1)
• UEME-AKM38 : MEng(Hons) Mechanical Engineering with Manufacturing and Management with Year long work placement (Year 1)
• UEME-AFM47 : MEng(Hons) Mechanical with Automotive Engineering (Year 1)
• UEME-AKM47 : MEng(Hons) Mechanical with Automotive Engineering with Year long work placement (Year 1)

 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.