MATH19662
Mathematics 1M2
10
Semester 2
Undergraduate
Level 1
Colin Steele
Unit coordinator
1
FHEQ level (Framework for Higher Education Qualifications) ' First part HE study/Bachelors '
European Credit Transfer & Accumulation System Rating : 5.0
<p>To provide a second-semester course in calculus and algebra to students with A-level mathematics or equivalent.</p>
<p>Knowledge and understanding: Be familiar with second order ordinary differential equations, partial differentiation, series and limits, partial differential equations and matrices.</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 school or in subsequent years.</p>
<p>5 Lectures: Second-order Ordinary Differential Equations. Linear Equations with constant coefficients; homogeneous and non-homogeneous cases; complementary functions and particular integrals, Special cases with non-constant coefficients.</p><p>3 Lectures: Partial Differentiation. Chain rule for partial differentiation. Total derivatives. Theory of errors. Coordinate Systems (Cartesian, Cylindrical, Spherical), change of variables.</p><p>3 Lectures: Series and Limits. Definition of Limits. L'Hopital's Rule. Sequences and Series; convergence; Power Series, Taylor and Maclaurin Series.</p><p>3 Lectures: Functions of Two Variables. Maxima, minima and saddle points. Taylor Series in Two variables.</p><p>3 Lectures: Second-order partial differential equations (wave, heat/diffusion, Laplace/Poisson. Solution by separation of variables.</p><p>4 Lectures: Matrices and Determinants: Definition of an m x n matrix. Matrix addition, subtraction, multiplication by a scalar, matrix multiplication; square matrices, determinants and properties; Solution of equations; inverse matrices.</p><p>3 Lectures: LinearAlgebra: LU Decomposition; solution of simultaneous equations; Gaussian Elimination; Cholesky's method.</p>
0
Other
20%
1
Written exam
80%
<p>Coursework 1 (week 5); Weighting within unit 10%</p><p> Coursework 2 (week 10); Weighting within unit 10%</p><p> End of semester 2 examination; Weighting within unit 80%</p>
MEng (Hons) Civil & Struct Eng
MEng (Hons) Civil & Struct Eng
First Year
Mandatory
N
<p>KA Stroud, Engineering Mathematics, Palgrave</p><p>E Kreyszig, Advanced Engineering Mathematics, Wiley</p><p>A Croft and R Davison, Mathematics for Engineers, Prentice Hall</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. </p><p>Please see Blackboard / course unit related emails for any further updates</p>