To motivate the students and to ignite their interest in abstract subjects like Mathematics, various applications of mathematics are discussed during lectures. These applications are related to nature around us, and different branches of engineering and sciences, which allow students to make logical connections between theory and practice.
Visualisation of Calculus
Instead of doing calculus on a piece of paper, our students are encouraged to visualise the calculus using software to better understand concepts. For example, current students were asked to write some practical examples of functions and to analyse these functions using Geogebra software. The students came up with many interesting practical applications of calculus such as calculating the total sale of Xiaomi mobiles in India, population growth, radioactive decay, the rate at which water comes out of a tap, voltage generated in a RLC circuit, Moore’s law, and the area of a steel frame.
Simulations play a key role in helping students better understand calculus. For examples, our students were given very simple simulations and were asked to run them and collect the data for different variables, and to fit a graph for the given data. The objective of this simulation was to introduce the concept of concavity, convexity, smoothness of the curves and to make the students learn about basic curve tracing.
To motivate the students and check how students apply the concepts that they have learnt in lectures, our students regularly complete group assignments. Some of the topics and mathematical challenges given to current students include:
• Mathematical analysis of the Angry Bird game with the help of Geogebra software
• Mathematical equations of the paths of each kind of bird, their functional representation, and some other properties of functions
• Mathematical and scientific analysis of size of fictional characters in movies like King Kong and the Austin Power series
• Mathematics in Nature
• Modelling of the path of straight stretch roller coaster with maximum thrill under certain fixed parameters
• Modelling of the memorisation rate of human brain and to validate the mathematical model by doing a survey on all students residing in the hostel
• Mathematical analysis of the back spin of a Table-Tennis ball
• Mathematical modelling of the progress of infectious disease