The course will discuss the three main classes of equations, elliptic, parabolic and hyperbolic. It is intended both for mathematics students continuing to honours work and for other students using mathematics at a high level in theoretical physics, engineering and information technology, and mathematical economics.

Topics to be covered will include fundamental solutions, maximum principles, regularity (smoothness) of solutions, variational problems, Holder and Sobolev spaces.

Note: This is an Honours Pathway Course. It emphasises mathematical rigour and proof.

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the concepts and language of partial differential equations and their role in modern mathematics and applied contexts
2. Analyse and solve complex problems using partial differential equations as functional and analytical tools
3. Apply problem-solving with partial differential equations to diverse situations in physics, engineering and other mathematical contexts

4. Ability to conduct some (limited) independent research under expert supervision.

• 3-4 written assignments involving problem-solving, proofs of theorems and extension of theory (60%; LO 1-4)
• Final exam (40%; LO 1-4)

36 lectures and tutorials by arrangement

A mark of 60 or more in MATH3320.