The year was 2001, but i don’t remember the exact date. It was fourth period, just after break and Mr Fawehinmi our Further Math teacher was running late. That was not unusual, what was unusual was the fact that the class was quiet, so quiet you could cut through the silence with a knife. Even though we were expecting a test, a class full of quiet SS3 Kings College boys without a teacher with a cane at hand was an unusual sight.
Mr Fawehinmi comes in smiling and says ‘Gentlemen, it’s time for your first form order’, he writes: TEST on the black board, we do as we are told after which he erases the black board and writes REVISION. At this point all of us including Uzopeters the class brainbox and gave him a standing ovation, the type that is only reserved for the bosses. Mr Fawehinmi still beaming like a magician who had just pulled off a hat-trick said ‘Calculus is simple, it’s all about solving problems, and life is about solving problems. Let me give you a few tips’. Although his statement didn’t make sense to me then, after that class calculus began to make sense to me.
After secondary school I went ahead to study Engineering Physics in a place called ‘White House’ in ‘Great Ife’ AKA Obafemi Awolowo University. To earn my degree, I had to solve a lot of problems: Classical, mechanical, quantum, electromagnetic and so on. What I discovered along the line was that I always had to use calculus, either I had to differentiate a problem or integrate an equation or invoke a formula which was derived by either by differentiation or integration. By the time I graduated I was calculated and done with calculus or so I thought as my first job had nothing to do with calculus.
Over the years I have come to realize that the reason I get paid is because of my ability to solve some of the problems my ’employer’ encounters on the way to his/her objective, hence Mr Fawehinmi’s statement ‘…life is about solving problems’ now makes sense to me. Over the years I have also observed a pattern in the way I solve problems at work and outside work. After I analyze the problem, i find a way to either disintegrate/decompose the ‘issue’ into smaller units for better handling or introduce an advantageous element to it or both. The first is called differentiation, while the second is called integration.
Differentiation and integration are two fundamental concepts in calculus. Calculus is the mathematical study of change. When confronted with a problem, we seek a solution i.e change which can be found through calculus. Calculus has a wide variety of applications in many fields such as science, economics, finance, engineering and so on. I personally think it cuts across every human endeavor.
- In biology, when a cell changes from a less specialized type to a more specialized type the process is called cellular differentiation, metamorphosis: the process through which a caterpillar becomes a butterfly is a classic example of an integral process.
- In marketing, the process of distinguishing a product or service from others to make it more attractive to targets thereby creating competitive advantage is called product differentiation.
- In Strategic management the arrangement in which a company owns and thereby optimizes its supply chain is called vertical integration, horizontal integration is when a company produces several related items.
- Social integration is the process of engaging members of a community in order to achieve active participation and peaceful social relations thereby fostering growth and development
- On a lighter note the evolution of Ice Cube from rapper to actor is called career integration
I could go on and on, but I hope you get the picture. Differentiation helps you focus and shed dead weight in order to achieve speed and effectiveness and is most important when survival is key. Integration helps you grow, develop and gain advantage and is most important when dominance is the goal.