MA34110 - PDEs

MT34110 - HDRh

General structure of the module

As with most mathematics modules, the course will be delivered via 22 lectures (two per week).

There will be four assignments throughout the course. While these do not count towards the final module mark, there is always a very strong correlation between final module mark and number of assignments handed in. I therefore encourage you very strongly to hand in your attempts at assignments in order to get feedback. Also, make sure you read my red squiggles on your work carefully and ask if there's any feedback you don't understand!

The module is assessed through a two-hour exam in the January exam period, which is worth 100% of the module mark.

Learning outcomes

On successful completion of this module students should be able to:
  1. classify partial differential equations and identify appropriate solution techniques;
  2. solve first order linear partial differential equations using the method of characteristics;
  3. demonstrate an ability to use the method of separation of variables to solve second order linear partial differential equations on rectangular domains;
  4. solve classical second order partial differential equations (wave, heat, Laplace’s equation) in infinite and semi-infinite domains and interpret their solutions;
  5. prove results concerning uniqueness of wave equation and heat equation solutions.

Overview of content

The following is an outline of the topics to be covered in this module:

  1. Fundamentals: definitions and examples, simple partial differential equations.
  2. First order equations: the method of characteristics.
  3. Boundary conditions: Dirichlet, Neumann, Robin, well-posedness and ill-posedness.
  4. Second order equations: classification, reduction to canonical forms.
  5. The wave equation: general solution, Cauchy problem, reflection principle, Duhamel principle, bounded string, energy and uniqueness.
  6. The heat equation: maximum principle, uniqueness, separation of variables,
    7. properties of solutions, the fundamential solution.

Further information

Definitive module information is available on the Aberystwyth University module pages.

General structure of the module

As with most mathematics modules, the course will be delivered via 22 lectures (two per week).

There will be four assignments throughout the course. While these do not count towards the final module mark, there is always a very strong correlation between final module mark and number of assignments handed in. I therefore encourage you very strongly to hand in your attempts at assignments in order to get feedback. Also, make sure you read my red squiggles on your work carefully and ask if there's any feedback you don't understand!

The module is assessed through a two-hour exam in the January exam period, which is worth 100% of the module mark.

Learning outcomes

On successful completion of this module students should be able to:
  1. classify partial differential equations and identify appropriate solution techniques;
  2. solve first order linear partial differential equations using the method of characteristics;
  3. demonstrate an ability to use the method of separation of variables to solve second order linear partial differential equations on rectangular domains;
  4. solve classical second order partial differential equations (wave, heat, Laplace’s equation) in infinite and semi-infinite domains and interpret their solutions;
  5. prove results concerning uniqueness of wave equation and heat equation solutions.

Overview of content

The following is an outline of the topics to be covered in this module:

  1. Fundamentals: definitions and examples, simple partial differential equations.
  2. First order equations: the method of characteristics.
  3. Boundary conditions: Dirichlet, Neumann, Robin, well-posedness and ill-posedness.
  4. Second order equations: classification, reduction to canonical forms.
  5. The wave equation: general solution, Cauchy problem, reflection principle, Duhamel principle, bounded string, energy and uniqueness.
  6. The heat equation: maximum principle, uniqueness, separation of variables,
    7. properties of solutions, the fundamential solution.

Further information

Definitive module information is available on the Aberystwyth University module pages.