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School of Mathematics

# 1M2 (MATH19662)

General Information
• Title: Mathematics 1M2
• Unit code: MATH19662
• Credit rating: 10
• Level: 1
• Pre-requisite units: 1M1 (MATH19661)
• Co-requisite units: None
• School responsible: Mathematics
• Member of staff responsible: Dr CDC Steele, Prof N Gray
Page Contents
Other Resources

## Unit specification

Aims
To provide a second-semester course in calculus and algebra to students with A-level mathematics or equivalent in school of MACE.
Brief description
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.
3 Lectures :- Partial Differentiation. Introduction. Chain rule for partial differentiation. Total derivatives. Theory of errors. Coordinate Systems (Cartesian, Cylindrical, Spherical), change of variables.
3 Lectures :- Series and Limits. Definition of Limits. L'Hopital's Rule. Sequences and Series; convergence; Power Series, Taylor and Maclaurin Series.
2 Lectures :- Functions of Two Variables. Maxima, minima and saddle points. Taylor Series in Two variables.
3 Lectures :- Second-order partial differential equations (wave, heat/diffusion, Laplace/Poisson. Solution by separation of variables.
5 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.
3 Lectures :- LinearAlgebra: LU Decomposition; solution of simultaneous equations; Gaussian Elimination; Cholesky's method.
Intended learning outcomes
Knowledge and understanding: Be familiar with second order ordinary differential equations, partial differentiation, series and limits, partial differential equations and matrices.
Intellectual skills: Be able to carry out routine operations involving the topics in the syllabus.
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.
Textbooks
KA Stroud, Engineering Mathematics, Palgrave
E Kreyszig, Advanced Engineering Mathematics, Wiley
Learning and teaching processes
Two lectures in weeks 1-11. One smallish-group tutorial in weeks 2-12. Revision Classes in week 12.
Lectures : 22
Tutorials : 11
Revision Classes: 2
Hours of private study : 65
Assessment
Coursework 1 (week 5); Weighting within unit 10%
Coursework 2 (week 10); Weighting within unit 10%
2 hour end of semester 2 examination; Weighting within unit 80%

## Arrangements

This is a first-year, second semester calculus course for students in the school of Mechanical, Aerospace and Civil Engineering. There are two lectures per week.

• The lectures for course 1M2 (MATH19662) for 2012-13 are as follows

• Wednesday 9 am : Renold/C16
• Friday 9 am : Renold/C16
• Lectures given by Prof N Gray
• Tutorials start in week 2. Each student is assigned to a group which meets once per week. Students should prepare their answers to the various questions in connection with the timetable.

Online course materials are available for this unit.