EP30.FSF1113 — Ordinary Differential Equations

This course provides a rigorous introduction to ordinary differential equations (ODEs) with applications to science, engineering, economics, and quantitative modeling. Beginning with first-order equations, the course develops fundamental analytical techniques such as integrating factors, separable equations, Bernoulli equations, and qualitative analysis of autonomous systems. Students will study second-order and higher-order linear differential equations, including homogeneous and nonhomogeneous problems, the Wronskian, complex and repeated roots, the methods of undetermined coefficients and variation of parameters, and applications to mechanical and electrical vibrations.

Emphasis is placed on mathematical modeling, solution interpretation, and understanding the relationship between theory and real-world phenomena. Numerical approximation methods such as Euler’s method are introduced to handle problems without closed-form solutions. Throughout the course, students will strengthen mathematical reasoning, develop skills in formulating and analyzing differential-equation models, and apply computational tools to support modeling and simulation. This course builds foundational competencies needed for advanced studies in applied mathematics, data science, optimization, quantitative finance, and engineering systems.

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.