MATH29661 10 Semester 1 Undergraduate Level 2 David Silvester Unit coordinator Mike Simon Unit coordinator 1 FHEQ level (Framework for Higher Education Qualifications) ' Middle part of Bachelors ' European Credit Transfer & Accumulation System Rating : 5.0 <p>The course unit aims to provide a second year course in mathematics and statistics.</p> <p>Knowledge and understanding: Demonstrate knowledge of the mathematical topics in the syllabus and their relevance to Mechanical, Aerospace, and Civil, Engineering.</p><p>Intellectual skills: Be able to carry out routine operations involving the topics in the syllabus.</p><p>Transferable skills and personal qualities: Have a set of tools and methods that can be applied in the courses given in the host department or in subsequent years.</p> <p>3 Multiple and Line Integrals. Construction and evaluation of double integrals including changing the order of the<br />integrations.&nbsp; Change of variable including the Jacobian. Introduction to triple integrals. Further Line integrals. Note 3</p><p>5 lectures: Vector Calculus. Scalar and Vector fields. Gradient, divergence and curl. Laplacian. Identities. Line and Surface integrals involving vectors. Vector integral theorems.</p><p>3 lectures: Laplace Transforms: Definition. Transforms and Inverse Transforms of Simple Functions. Transforms of derivatives and integrals. Convolution, Solution of Ordinary Differential Equations using Laplace Transforms.</p><p>4 lectures: Numerical Methods. Interpolation and Least Squares approximation. Further numerical integration, integration rules, numerical integration where interval or function becomes infinite. Solution of systems of non-linear algebraic equations.</p><p>8 lectures: General notion of a random variable, including its definition and the range space.<br />Discrete random variables &ndash; definition and explanation;&nbsp; probability mass function (pmf);&nbsp; discrete Uniform distribution;&nbsp; Binomial distribution;&nbsp; mean and variance of discrete random variables.<br />Continuous random variables &ndash; definition and explanation; probability density function (pdf);&nbsp; Uniform distribution;&nbsp; Exponential distribution;&nbsp; Normal distribution;&nbsp; mean and variance of continuous random variables.<br />Linear transformations of random variables. ie. Y=aX+b.&nbsp; Mean and variance of Y.<br />The cumulative distribution function for discrete and continuous random variables;&nbsp; calculating Normal probabilities (standardising), characteristic load and strength.<br />Normal approximation to the Binomial distribution. Application to quality control.</p> 0 Other 20% 1 Written exam 80% <p>Coursework (week 9) Weighting within unit 20%</p><p>Examination (semester 1) Weighting within unit 80%</p> MATH19662 Mathematics 1M2 Pre-Requisite Compulsory MEng (Hons) Civil & Struct Eng MEng (Hons) Civil & Struct Eng Second Year Mandatory N <p>E. Kreysig, Advanced Engineering Mathematics, John Wiley</p><p>G James et. al., Modern Engineering MathematicsPearson</p><p>G James et. al., Advanced Modern Engineering MathematicsPearson</p><p><a href="http://www.maths.manchester.ac.uk/study/undergraduate/information-for-current-students/service-teaching/helm/">HELM</a> (Helping Engineers Learn Mathematics)</p> Lectures 24 Tutorials 11 0 65 <p>This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.&nbsp;&nbsp;</p><p>Please see Blackboard / course unit related emails for any further updates</p>