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ME10305: Mathematics 2

Credits: 6
Level: Certificate (FHEQ level 4)
Period: Semester 2
Assessment: EX 100%
Supplementary Assessment: ME10305 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:
* Solve certain classes of ODE.
* Perform Laplace Transforms and their inverse.
* Determine probabilities of events and sequences of events.
* Determine probabilities and find means and standard deviations of both discrete and continuous probability distributions.
* Statistical testing.
* Find eigenvalues and eigenvectors of square matrices.
* Perform least-squares fitting of data.

Skills:
Numeracy; working independently.

Content:
Ordinary differential equations: classification; reduction to first order form; 1st order nonlinear equations, variables-separable equations, linear constant coefficient equations. Laplace Transforms: definition; examples; transforms of derivatives; unit pulse, impulse and step function; shift theorems in s and t; solution of linear constant-coefficient ODEs, convolution theorem. Probability: trial, outcome, sample space and event; use of Venn diagrams; simple probability; complementation and addition rules; conditional probability; independent events; sampling; probability relating to sequences of events. Probability distributions: discrete and continuous distributions; mean, median, mode, percentiles and standard deviation; Poisson distribution; normal distribution. Statistics: hypothesis testing. Matrices: Gaussian elimination; eigenvalues and eigenvectors. Miscellaneous topics: least squares fitting of data.
Programme availability:

ME10305 is Compulsory on the following programmes:

Department of Electronic & Electrical Engineering
• UEXX-AFB02 : BEng (hons) Integrated Mechanical and Electrical Engineering (Full-time) - Year 1
• UEXX-AKB02 : BEng (hons) Integrated Mechanical and Electrical Engineering (Thick Sandwich) - Year 1
• UEXX-AFM02 : MEng (hons) Integrated Mechanical and Electrical Engineering (Full-time) - Year 1
• UEXX-AKM02 : MEng (hons) Integrated Mechanical and Electrical Engineering (Thick Sandwich) - Year 1
Department of Mechanical Engineering
• UEME-AFB26 : BEng (hons) Aerospace Engineering (Full-time) - Year 1
• UEME-AKB26 : BEng (hons) Aerospace Engineering (Thick Sandwich) - Year 1
• UEME-AFB01 : BEng (hons) Automotive Engineering (Full-time) - Year 1
• UEME-AKB01 : BEng (hons) Automotive Engineering (Thick Sandwich) - Year 1
• UEME-AFB16 : BEng (hons) Mechanical Engineering (Full-time) - Year 1
• UEME-AKB16 : BEng (hons) Mechanical Engineering (Thick Sandwich) - Year 1
• UEME-AFB41 : BEng (hons) Mechanical Engineering with Advanced Design and Innovation (Full-time) - Year 1
• UEME-AKB41 : BEng (hons) Mechanical Engineering with Advanced Design and Innovation (Thick Sandwich) - Year 1
• UEME-AFB38 : BEng (hons) Mechanical Engineering with Manufacturing and Management (Full-time) - Year 1
• UEME-AKB38 : BEng (hons) Mechanical Engineering with Manufacturing and Management (Thick Sandwich) - Year 1
• UEME-AFM04 : MEng (hons) Aerospace Engineering (Full-time) - Year 1
• UEME-AKM04 : MEng (hons) Aerospace Engineering (Thick Sandwich) - Year 1
• UEME-AFM01 : MEng (hons) Automotive Engineering (Full-time) - Year 1
• UEME-AKM01 : MEng (hons) Automotive Engineering (Thick Sandwich) - Year 1
• UEME-AFM16 : MEng (hons) Mechanical Engineering (Full-time) - Year 1
• UEME-AKM16 : MEng (hons) Mechanical Engineering (Thick Sandwich) - Year 1
• UEME-AFM41 : MEng (hons) Mechanical Engineering with Advanced Design and Innovation (Full-time) - Year 1
• UEME-AKM41 : MEng (hons) Mechanical Engineering with Advanced Design and Innovation (Thick Sandwich) - Year 1
• UEME-AFM38 : MEng (hons) Mechanical Engineering with Manufacturing and Management (Full-time) - Year 1
• UEME-AKM38 : MEng (hons) Mechanical Engineering with Manufacturing and Management (Thick Sandwich) - Year 1

NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.