3 x 50-minute lectures weekly
2 x 50-minute tutorials weekly
Enrolment not permitted
MATH3712 has been successfully completed
Assumed knowledge
An understanding of fundamental concepts of multivariable calculus.
Topic description

This topic includes: Linearity and superposition principle, classification of linear partial differential equations of second order; one dimensional wave equation, initial value problem, clamped and free boundary conditions, non-homogeneous wave equation, uniqueness and stability of solution; three-dimensional wave equation, Kirchhoff's formula; heat equation, initial value problem, clamped and free boundary conditions, the maximum principle, uniqueness and stability of solution; three-dimensional heat equation. Laplace equation, Green's formulas, Dirichlet and Neumann problems, the maximum principle and uniqueness of solution; Green's function. Fourier transform in n dimensions, generalized functions and generalized solutions of equations. Fredholm theory of integral equations.

Educational aims

This topic aims to equip students with the skills needed to solve mathematical problems in the theory of partial differential equations. The focus is on both the application of mathematical ideas to practical problems and on rigorous understanding of mathematical principles.

Expected learning outcomes
On completion of this topic you will be expected to be able to:

  1. Understand how a variety of problems from physical and other sciences can be formulated as partial differential equations
  2. Solve a variety of initial value and boundary problems of mathematical physics
  3. Understand and interpret physical meaning of mathematical results
  4. Get a strong foundation in theoretical aspects of partial differential equations
  5. Apply Fourier series and Fourier transform to solution of mathematical problems