Enhancing Conceptual Understanding through Peer-Led Algorithm Design for Heat and Wave Equations 

Selection of Peer Instructors

Conceptual Presentation

Algorithm Development

Implementation and Demonstration

Interactive Learning Session

Reflection and Feedback

This pedagogy was designed to promote active learning through peer-led instruction, where two students acted as facilitators to explain and demonstrate key concepts in Differential Equations, with a particular focus on Cauchy Differential Equations.

The session began with the peer instructors presenting a conceptual overview of ordinary differential equations (ODEs), including their classification, order, degree, and relevance in modeling dynamic systems. They then introduced Cauchy (Euler–Cauchy) differential equations, emphasizing their structure, solution strategies, and applications in engineering and physics.

Following the theoretical introduction, the peer instructors guided the class through the step-by-step process of solving Cauchy differential equations using substitution techniques and reduction to equations with constant coefficients. They further demonstrated how these solutions can be implemented computationally using Python/MATLAB to visualize behaviors of solutions under varying initial conditions.

The interactive format allowed students to discuss, question, and experiment with the methods, deepening their analytical understanding. This collaborative learning environment encouraged peer-to-peer engagement and critical thinking. Through this approach, students strengthened their mastery of differential equations while simultaneously developing computational and problem-solving skills essential for advanced mathematical modelling. 

5 Members

Chart Papers / Drawing Sheets – for visual presentation of the Heat and Wave Equations.

Markers, Sketch Pens, and Crayons – for highlighting key points and creative illustration on charts.

Reference Materials (Textbooks, Notes, Online Resources) – to gather theoretical and algorithmic content.

Stationery Items (Scissors, Glue, Rulers, Sticky Notes, etc.) – for preparing and assembling the charts.

Laptop / Computer – for developing, testing, and displaying algorithms using Python.

Projector / Classroom Display Boards – to present the charts and demonstrate computational results.

Internet Connectivity – for research, accessing online tutorials, and debugging program codes.

Students’ Collaboration and Teamwork – as the key human resource for explaining concepts and engaging peers.

Faculty Guidance – for supervision, conceptual support, and evaluation of the activity.