2005/06 Undergraduate Module Catalogue
MATH3414 Analytic Solutions of Partial Differential Equations
15 creditsClass Size: 100
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2005/06
Pre-requisitesMATH2360 or MATH2420 or equivalent.
This module is approved as an Elective
ObjectivesTo provide an understanding of, and methods of solution for, the most important types of partial differential equations that arise in Mathematical Physics. On completion of this module, students should be able to: a) use the method of characteristics to solve first-order hyperbolic equations; b) classify a second order PDE as elliptic, parabolic or hyperbolic; c) use Green?s functions to solve elliptic equations; d) have a basic understanding of diffusion; e) obtain a priori bounds for reaction-diffusion equations.
The majority of physical phenomena can be described by partial differential equations (e.g. the Navier-Stokes equation of fluid dynamics, Maxwell's equations of electromagnetism). This module considers the properties of, and analytical methods of solution for some of the most common first and second order PDEs of Mathematical Physics. In particular, we shall look in detail at elliptic equations (Laplace?s equation), describing steady-state phenomena and the diffusion / heat conduction equation describing the slow spread of concentration or heat. The topics covered are: First order PDEs. Semi-linear and quasi-linear PDEs; method of characteristics. Characteristics crossing. Second order PDEs. Classification and standard forms. Elliptic equations: weak and strong minimum and maximum principles; Green's functions. Parabolic equations: exemplified by solutions of the diffusion equation. Bounds on solutions of reaction-diffusion equations.
Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for informationLectures: 26 hours. 7 examples classes.
Methods of assessment
Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for informationOne 3 hour examination at end of semester (100%).
Reading listThe reading list is available from the Library website
Last updated: 13/05/2005
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