Mathematical Modeling of Physical Phenomena from Capacitors to Cosmology
The second LUMS Math Circle session of the year, titled "Mathematical Modeling of Physical Phenomena from Capacitors to Cosmology", was held on September 13, 2024. Led by Dr. Rizwan Khalid and Dr. Ammar, the session emphasized the critical role of observations in the scientific method.
Dr. Rizwan opened with a clear explanation of the scientific process: starting with a question, making observations, formulating hypotheses, and then conducting experiments to test those hypotheses. He stressed the importance of keen observation skills and highlighted how this step underpins successful scientific inquiry. To engage the students, Dr. Rizwan introduced curve fitting as a practical example of mathematical modeling. Drawing on the story of renowned Pakistani physicist Dr. Abdus Salam, he illustrated how careful observation can lead to groundbreaking discoveries.
Next, Dr. Ammar captivated the audience by presenting the students with an equation modeling the behavior of voltage across a capacitor during charging and discharging. The students, many of whom were encountering such a problem for the first time, were eager to learn. They were then given gadgets, including multimeters, to carry out a hands-on activity to measure the voltage across a capacitor using the formula V_C=9−V_R. This interactive exercise provided an exciting introduction to real-world applications of mathematical modeling.
In the final part of the session, Dr. Rizwan took students on a journey back to ancient Greece, explaining how early scientists used parallax to estimate distances in the universe. He discussed the limitations of the method, which led the Greeks to believe the universe was smaller than it truly is. The students were fascinated to learn how modern science has overcome these limitations, using techniques like luminosity measurements to calculate the distances of far-off stars and galaxies.
The session concluded with a lively discussion and certificate distribution ceremony, leaving students inspired by the practical applications of mathematics in understanding the physical world.
Special thanks to Ms. Noreen Sohail, Mr. Qamar Hussain and Mr. Javaid Qayyum (the author of this email) for their continued organizational support.
Here are some highlights from the event:
