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Module MA3425: Partial Differential Equations I

Credit weighting (ECTS)
5 credits
Semester/term taught
Michaelmas term 2014-15
Contact Hours
11 weeks, 3 lectures per week
Lecturer
Prof. Paschalis Karageorgis
Learning Outcomes
On successful completion of this module, students will be able to:
  • Give and use basic definitions, e.g. order, linear,type of PDE etc.;
  • State correctly and apply to examples the basic facts about the Wave Equation in one space dimension: Energy conservation (differential, local and global forms), existence and uniquess of solutions, finite speed of propagation. Solve the initial value problem for given data using the explicit solution;
  • State correctly and apply to examples the basic facts about the Heat Equation in one space dimension: Maximum Principle (local and global versions), Existence and uniqueness of bounded solutions, smoothing, decay of solutions. Solve the initial value problem for given data using the explicit solution;
  • State correctly and apply to examples the basic facts about the Laplace Equation in two space dimensions: Maximum Principle (local and global versions), Existence and uniqueness of solutions to the Dirichlet problem. Solve boundary value problems using the Poisson formulae;
Module Content
  • Module Content;
  • Classification of partial differential equations
  • Wave, Heat and Laplace Equations in low dimensions
 
Module Prerequisite
MA2223 - Metric Spaces, MA2224 - Lebesgue Integral, MA2326 - Ordinary Differential Equations
Assessment Detail
This module will be examined jointly 2 hour examination in Trinity term. Continuous assessment will contribute 10% to the final grade for the module at the annual examination session.