Partial differential equations arise from the mathematical modelling of a wide range of problems in biology, engineering, physical sciences, economics and finance. Therefore, they form an essential part of the mathematical background required for engineering and physical sciences. This course introduces students to the modern theory and methods of partial differential equations. It provides the students with the skills to formulate partial differential equations for modelling real-world problems, the knowledge to solve them using fundamental analytical and numerical methods, and the ability to interpret the results in the relation to the modelling context.
Availability2021 Course Timetables
- Semester 2 - 2021
On successful completion of the course students will be able to:
1. Build mathematical models of relevant real-world problems based on partial differential equations in studying differential equations.
2. Classify second order partial differential equations, apply analytical methods to solve them, and physically interpret the solutions.
3. Apply numerical methods to solve practical partial differential equations and implement them in computers.
4. Interpret and communicate solutions in relation to the underlying modelling problem.
5. Analyse the consistency, stability and convergence properties of numerical methods.
- Modelling with partial differential equations.
- Classical solution techniques: method of characteristics, separation of variables and Fourier series, fundamental solution and Green's function, transform methods.
- Qualitative analysis and weak solution: maximum and minimum principles, well-posedness, weak solution.
- Numerical methods for partial differential equations: consistency, stability and convergence.
Written Assignment: Assignments
Formal Examination: End of Semester Exam
Face to Face On Campus 3 hour(s) per Week for Full Term
Tutorial and computer lab work will be integrated with lecture material as required.
The University of Newcastle acknowledges the traditional custodians of the lands within our footprint areas: Awabakal, Darkinjung, Biripai, Worimi, Wonnarua, and Eora Nations. We also pay respect to the wisdom of our Elders past and present.