Calculus is an important branch of Mathematics. Calculus is studied in three parts. First part is single variable calculus, second part is multi-variable calculus and third part is differential calculus. In our daily life we come across problems which belong to single variable calculus or can be solved by methods applied by single variable calculus. But if we have to deal with complex problems we have to come across multi-variable calculus and differential equations. A little bit of differential equations is taught in single variable calculus because we come across simple differential equations in physics. For example to describe motion of springs and simple pendulum which is simple harmonic.
In single variable calculus topics covered are differentiation, integration, application of differentiation and application of integration. Application of differentiation is completely dependent upon differentiation. Similarly application of integration is dependent upon integration. Integration is reverse process of differentiation. But integration of all functions don't exist. So we have to study differentiation first to have a view of what can be integrated. Also integration requires practice. When we integrate a lot of problems we develop skills to integrate.
Differentiation is related to rate. Rate is found of something which changes. Now the change can be constant or variable. We come to know about change by finding the rate. Here differentiation comes in handy. We can find the rate if we can express a method by which we can check change in one variable w.r.t other variable. Relationship between two variables is known as a map. A class of mapping is known as functions. Calculus is full of functions.
Integration is related to sum. Integration can be used to find sum, area, etc.
In single variable calculus topics covered are differentiation, integration, application of differentiation and application of integration. Application of differentiation is completely dependent upon differentiation. Similarly application of integration is dependent upon integration. Integration is reverse process of differentiation. But integration of all functions don't exist. So we have to study differentiation first to have a view of what can be integrated. Also integration requires practice. When we integrate a lot of problems we develop skills to integrate.
Differentiation is related to rate. Rate is found of something which changes. Now the change can be constant or variable. We come to know about change by finding the rate. Here differentiation comes in handy. We can find the rate if we can express a method by which we can check change in one variable w.r.t other variable. Relationship between two variables is known as a map. A class of mapping is known as functions. Calculus is full of functions.
Integration is related to sum. Integration can be used to find sum, area, etc.
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