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Module MA3425: Partial differential equations I

Credit weighting (ECTS)
5 credits
Semester/term taught
Michaelmas term 2012-13
Contact Hours
11 weeks, 3 lectures including tutorials per week
Lecturer
Prof. John Stalker
Learning Outcomes
On successful completion of this module, students will be able to:
  • Give and use basic definitions, e.g. order, linear, etc. Apply the concepts of symmetries and in variant solutions, at least for the Wave, Heat and Laplace Equations;
  • 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. Students should also able to employ the method of reflection to solve simple boundary value problems;
  • 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. Students should also be able to employ the method of reflection to solve simple boundary value problems;
  • 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. Students should also be able to employ the method of reflection to solve simple boundary value problems;
  • 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 with MA3426 in a 3-hour examination in Trinity term, except that those taking just one of the two modules will have a 2 hour examination. However there will be separate results for MA3425 and MA3426. Continuous assessment will contribute 10% to the final grade for the module at the annual examination session.