Methods of Applied Mathematics

MATH35041 Methods of Applied Mathematics 20 Semester 1 Undergraduate Level 3 Neil Morrison Unit coordinator Paul Glendinning Unit coordinator 1 FHEQ level (Framework for Higher Education Qualifications) ' Middle part of Bachelors ' European Credit Transfer & Accumulation System Rating : 10.0 This course unit provides students with the methodology to study problems which arise in applied mathematics.  Often, the analytical solution to such a problem involves approximation in terms of a small parameter. We consider asymptotic expansions, such that the error made is controlled. Throughout, the focus will be on examples and on applying the mathematical methods in a physical context.  The course is therefore most suitable for students with strengths and interests in applied mathematics.  Fluency in calculus and ODEs will be beneficial. This course unit introduces students to important topics in applied mathematics, developing their understanding of asymptotic methods and calculus of variations. The syllabus is motivated by physical applications of historical importance. <ul> <li>Apply asymptotic methods to obtain perturbation expansions of algebraic equations.</li> <li>Compute asymptotic expansions of integrals containing a parameter.</li> <li>Calculate asymptotic solutions to ODEs containing a parameter, matching the inner and outer solutions as appropriate.</li> <li>Interpret variational problems and solve the corresponding Euler-Lagrange equations.</li> <li>Calculate solutions to standard variational problems (e.g. the brachistochrone, Fermat’s principle, geodesics, minimal surface, the isoperimetric problem, the hanging chain).</li> <li>Formulate equations of motion in classical mechanics from a Lagrangian, via Hamilton’s Principle and describe solutions to mechanical problems using the Euler-Lagrange equations and/or perturbation theory.</li> <li>Estimate eigenvalues via the Rayleigh-Ritz method and apply to physical problems.</li></ul> 1 Written exam 80% 3 Report 20% Individual feedback via marking comments, and cohort feedback document circulated.   MATH11422 ODEs and Applications Pre-Requisite Compulsory MATH11412 Introduction to Ordinary Differential Equations Pre-Requisite Compulsory MATH24420 Partial Differential Equations & Vector Calculus Pre-Requisite Compulsory PHYS20171 Mathematics of Waves and Fields Pre-Requisite Compulsory MATH10222 Calculus and Applications A Pre-Requisite Compulsory MATH10232 Calculus and Applications B Pre-Requisite Compulsory MATH20401 Partial Differential Equations and Vector Calculus A Pre-Requisite Compulsory MATH35041 Pre-Requisites: MATH11412/22 and MATH24420 (or PHYS20171)PHYS20171 is an acceptable alternative for those Maths-Physics students who took that unit instead of MATH24420 N Lectures 33 Tutorials 11 0 156