Calculus
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Calculus is one of the main branches of mathematics built on the basic concepts of both algebra and geometry. The study of Calculus is crucial in a number of fields like physics and Engineering sciences. It plays a significant role in several areas of scientific research and is a powerful tool for understanding complex phenomena. Calculus finds great use in economics and certain studies in medicine as a means to prepare a mathematical model to a problem requiring an optimum solution.
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Differential and integral calculus
Calculus has two complementary domains, namely differential calculus and integral calculus.
- Differential calculus deals with the instantaneous rates of change of quantities with respect to other varying quantities. The so-called "differential coefficient" can be used as a rate measurer. Differential calculus can also be used to study the local behaviour of functions. The differentiation of a function thus gives the instantaneous slope of the graph of a function.
- On the other hand, integral calculus deals with the study of the addition of quantities, such as the volume or area to be observed. Integration is the reverse process of differentiation.
Examples of problems in calculus
Problems in calculus can be vastly varied, considering the fact that it is used in several fields of knowledge. Typical problems in both differential and integral calculus are listed below:
Differential calculus
- Finding the instantaneous speed of a vehicle. The speed as measured by the speedometer is the derivative of the car's distance travelled, as a function of time. The distance is measured by an odometer.
- Finding the optimal quantity of goods that a company should produce to attain maximum profit.
Integral Calculus
- This is used to compute a quantity that is equal to the sum of a large number of smaller quantities, eg. the area under a curve is the sum total of several small 'areas' that can be integrated over central limits.
- Integral calculus can be used in fluid mechanics to find the amount of pumped fluid when there is a fixed input power but varying pressure and losses.