EP30.FSF1112 — Partial Differential Equations

This course provides a rigorous introduction to Partial Differential Equations (PDEs) with a focus on both theoretical foundations and analytical solution techniques. Students will study the origins of PDEs from physical, economic, and engineering models, and learn the classification of first- and second-order equations. Fundamental topics include semi-linear and quasilinear first-order equations, weak derivatives, distributions, and constant-coefficient second-order PDEs.

The course develops essential tools such as the Fourier transform, tempered distributions, Duhamel’s principle, and separation of variables. Students will explore boundary-value problems, convergence of Fourier series, symmetric operators, and orthogonality in inner product spaces. Applications to diffusion, wave propagation, potential theory, finance, and data-driven modeling are emphasized throughout the course. Both classical and weak solution frameworks are introduced to prepare students for advanced study. The course also enhances computational thinking through numerical approximation and visualization of PDE solutions. By the end of the course, students will be able to model, analyze, and interpret real-world phenomena governed by PDEs using analytical, numerical, and conceptual tools.

Requirements for Final Examination

Students are allowed to take the final/terminal exams (50%) if their attendance score (10%) is 5 or higher (on a 10-point scale).

See Appendix 2, Rubric 1 for attendance evaluation.

Requirements for Class Attendance

Students are responsible for attending all classes. In case of absence due to force majeure, students must provide sufficient and reasonable proof. For each absence, 1 point will be deducted from the attendance score. Students who miss more than 3 classes, with or without valid reasons, will be considered as failing to complete the course and must re-register.

Students will be awarded points for constructive comments. These points will be added to attendance and group assignment scores.

Groups that do not submit their group work will receive a score of 0. Late submissions will incur a deduction for each day they are late.

Requirements for In-class Behaviour

The course is conducted on the principle of mutual respect between learners and lecturers. Any behavior that disrupts the teaching and learning process is strictly prohibited.

Students must arrive on time for class. Those who are more than 10 minutes late will not be allowed to attend. Noise and other disturbances that affect the learning process are not permitted.

Laptops and tablets may only be used for taking notes and performing calculations related to lectures and exercises. Use for any other purpose is strictly prohibited.