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Courses in Mathematics and Statistics Level 1 Modules Level 2 Modules Level 3 Modules Level 4 Modules Level 5 Modules Honours timetable 2011/2012 Sem. 1 2011/2012 Sem. 2 2012/2013 Sem. 1 & Sem. 2 2013/2014 Sem. 1 & Sem. 2

MT2001 MATHEMATICS This is a core second level mathematics module which must be taken by anyone planning to pursue Honours level material in Mathematics, Statistics or Physics. Aims To extend the knowledge and skills gained by students in the module MT1002 in preparation for Honours study. In particular - to enhance their skills and understanding of calculus to include functions of several variables; - to develop an appreciation of basic ideas in Linear Algebra. Objectives By the end of the course a student should be able to demonstrate: - how to determine the Taylor series of a function and estimate the error associated with a Taylor polynomial; - an understanding of the concepts of continuity and differentiability of functions of several variables; partial differentiation and an appreciation of the difference between partial and ordinary differentiation; - how to determine the local behaviour of surfaces at stationary points; - how to determine integrals over areas and volumes (and when necessary use different co-ordinate systems including cylindrical and spherical polars); - an ability to work with the fundamental concepts of vector space theory; - an ability to manipulate matrices in order to find inverses and determinants; - how to determine the eigenvalues and eigenvectors of a square matrix (and diagonalisation when appropriate); - how to obtain a Fourier series representation of simple function and interpret its properties. Textbooks Advanced Engineering Mathematics E Kreyszig; Wiley Advanced Engineering Mathematics, A Jeffrey; Harcourt/Academic Press; 2002. Calculus (6th Edition) E W Swokowski, M Olinick, D Pence; PWS; 1994. [This book is out of print, but may be available second-hand.] H Anton; Elementary Linear Algebra, Wiley; 1991 Lectures, practicals and tutorials The average load, in hours per week, is as follows: Lectures: 5 Practicals: 1 Tutorials: 1 These figures do not include the revision and exam period at the end of each semester. Assessment 30% of the assessment mark is from continuous assessment during the semester. The remainder is from a 3 hour exam at the end of the semester. Re-assessment is entirely by a 3 hour exam in August. Prerequisites MT1002 Availability This module is taught every year in both Semester 1 and Semester 2 at 12.00. Lecturers First Semester: Dr A P Naughton (Module coordinator), Dr C V Tran, Dr Y Peresse Second Semester: Dr S Huczynska (Module coordinator), Prof D G Dritschel, Dr A P Naughton Click here for access to past examination papers for this module. Click here to see the University Course Catalogue entry. Revised: PMH (February 2013)