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Module MA342T: Partial Differential Equations
- Credit weighting (ECTS)
- 5 credits
- Semester/term taught
- Michaelmas term 2018-19
- Contact Hours
- 11 weeks, 3 lectures 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,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
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- Module Content;
- Classification of partial differential equations
- Wave, Heat and Laplace Equations in low dimensions
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- Module Prerequisite
- MA2223 - Metric Spaces, MA2224 - Lebesgue Integral, MA2326 - Ordinary Differential Equations (Students who do not have the pre-requisites may still qualify to take module - please contact Prof John Stalker)
- Assessment Detail
- This module will be examined jointly 2 hour examination in Michaelmas term. Continuous assessment will contribute 10% to the final grade for the module at the annual examination session.