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Calculus is one of the most important branches of mathematics. Calculus deals with continuous chance and has two major concepts: integrals and derivatives. Calculus is a branch of mathematics that uses mathematical models to get optimal solutions. It helps in understanding change between values through a related function. Calculus focuses on some of the most important topics covered in mathematics, such as;
- Differentiation
- Integration
- Limits
- Functions
Calculus was developed by Newton and Leibniz and deals with studying the rate of change. Calculus is classified into;
- Differential Calculus – Differential calculus is a branch of calculus that focuses on finding a solution to the problem of finding the rate of change of a function compared to other variables. To get the desired solution, derivatives are used to calculate the minima and maxima values of the function in question. In calculus, differentials help study the limit of quotient and deal with variables such as x and y. The process of finding derivatives in calculus is called differentiation.
- Integral Calculus – Integral calculus is described as the study of integrals and all the associated properties. A good example is calculating an area under a curve for a function. Integration is the opposite of differentiation. Therefore if a solution in differentiation is achieved by dividing apart into small portions, then integration is achieved by collecting small portions to have a whole portion.
Topics in Calculus
There are three topics in calculus that are categorized based on the complexity of the concepts. Calculus is made up of three topics which are;
| Precalculus | Precalculus is a topic in calculus that includes algebra and trigonometry, which is generally designed to prepare students for calculus. In Precalculus, the focus is on the study of advanced math concepts which involve quantitative reasoning. Topics covered in Precalculus include;
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| Calculus 1 | In calculus 1, the topics covered are topics that focus on differential calculus and concepts such as continuity and limits. In Calculus 1, the main topics covered here include;
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| Calculus 2 | In calculus 2, the focus is on mathematical study of change as introduced in calculus 1. The main topics in calculus 2 include;
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Application of calculus
- Calculus is used in analyzing systems to find the optimal solutions in predicting the future of a condition for a function.
- Calculus is used in modeling different concepts such as birth rates, death rates, reaction rates, motion, electricity, etc.
- Calculus is the popular language of economists, engineers, and architects as they use the different concepts in calculus in determining different shapes in construction.
- Calculus concepts are used in real life in evaluating survey data, business planning, the safety of vehicles, and even checking the changing condition of a system, which may affect us.