Department of Mathematical Sciences, Unit Catalogue 2010/11 |
MA20223: Partial differential equations and continuum mechanics |
 Credits:
| 6 |
| Level:
| Intermediate |
| Period: | This unit is available in... |
| Semester 2 |
| Assessment:
| EX100 |
| Supplementary Assessment: | Supplementary assessment information not currently available (this will be added shortly) |
| Requisites:
| While taking this unit you must take MA20219 and before taking this unit you must take MA10207 and take MA10208 and take MA10209 and take MA10210 and take MA20216 and take MA20218take MA20220 or equivalent units from MA10001 - MA10006. |
| Description:
| Aims: To introduce three basic classes of linear PDEs as characterised by the Laplace, heat and wave equations and the method of separation of variables for their solution. To introduce basic concepts and methods of continuum mechanics and to illustrate the significance of PDEs in this context. Learning Outcomes: After taking this unit, students should be able to: * Demonstrate familiarity with the basic properties of Fourier series. * Solve the Laplace and Helmholtz equations, the wave equation and the heat equation in simple domains using separation of variables or Laplace transform. * Show familiarity with basic concepts and equations of continuum mechanics and be able to solve the latter in certain idealised situations involving solids and fluids. * Write the relevant mathematical arguments in a precise and lucid fashion. Skills: Numeracy T/F A Problem Solving T/F A Written and Spoken Communication F (in tutorials). Content: Fourier series: Formal introduction of Fourier series, Fourier convergence theorem; Fourier cosine and sine series. Partial differential equations: classification of linear second order PDEs; Laplace and Helmholtz equations in simple 2D and 3D domains (e.g. rectangular, circular, cylindrical); heat equation and wave equation in one space dimension; solution by separation of variables; solution of the heat equation by Laplace transform. Continuum mechanics: deformation and flow; Lagrangian and Eulerian specifications; material time derivative, acceleration; constitutive equations; balance laws, the continuity equation, equations of motion and equilibrium; simple examples including potential flow and homogeneous deformations. |