Computers have invaded almost all walks of our life and transformed them so much that it is now difficult to imagine a world without them. Yet, the use of computers in our educational system, especially at the school level, is less than optimal.
While students of science learn a lot of mathematics and study how it can be used to solve problems in science, they do not learn much about how computers can be used to solve the same problems. This is in spite of the fact that these students are also learning computer science at the same time.
The importance of using computers to learn science cannot be overemphasised. To paraphrase an old Chinese saying, “I hear (a lecture) and I forget. I see (an experiment) and I remember. I compute and I understand.”
Most students and teachers browse the Internet to locate animations or simulations which would lead to a better understanding of a concept. However, asking a student to program a simulation from scratch would improve his programming skills as well as his understanding of scientific concepts.
At this point, many of our teachers may object that they do not want their students to get bogged down with the intricacies of the syntax of a programming language. However, many new tools for programming and visualisation are widely available (some of them free) and the learning curve associated with using these tools is not so steep.
Matlab and Mathematica are two widely used software packages for scientific computation and visualisation. These software packages make the job of programming somewhat simple as compared to a language like ‘C’. They also provide visualisation tools for creating two-dimensional and three-dimensional plots which lead to a drastic improvement in our understanding of various concepts.
Software packages such as the ones mentioned above are also freely available on the Internet. Scilab and Octave can be downloaded. Using computer programs to simulate physical systems not only helps a student understand concepts which he has already learnt, but also enables him or her to explore new scenarios and problems. For example, projectile motion is taught at school level and everybody learns that the trajectory of a projectile is a parabola.
Visualise theory
All problems which students normally solve concerning projectile motion come with a rider that “air resistance is ignored.” It is natural for a student to wonder about the effects of resistance of air on the motion of a projectile. After all, in the real world, all projectiles are subject to air resistance!
The motion of a projectile in the presence of air resistance is a problem which is difficult to solve using the mathematical tools normally available to a student, but it can be computed and visualised easily using a computer.
The trajectory of a projectile subject to air resistance may be difficult to obtain through experiments, but can be done easily using a computer ‘experiment’, or, simulation. Of course, the results of such a computer simulation depend crucially on how one models the air resistance.
In a similar fashion, we can forego many of the assumptions which are usually made in solving typical textbook problems. This will help us to bridge the gap between textbook problems and real-life problems.
Word of caution
While emphasising the power of computer simulations we should also be mindful of their limitations. Any computer uses a limited number of bits to store the numerical value of a physical quantity. Irrational numbers cannot be stored in a computer and many rational numbers cannot be represented exactly. The difference between the actual numerical value of a quantity and its value as stored in a computer is a measure of the error in the computation. This error can increase as the computation proceeds over many stages.
Hence we should be sure that the results of the computation are not predominantly due to the errors in the computation. Traditional mathematical tools are essential to know the magnitude of the errors in a computation. Hence traditional mathematics is all the more important in this scenario.
Learning to solve problems using only pen and paper does have its value, but combining it with computer simulations will expand the frontiers of our understanding.
The writer is associate professor, BITS – Pilani, Hyderabad.