Calculus
Calculus, put plainly, is the study of rates of change. It focus on the relationship between a function's output and how fast the output changes given an input. For example calculus can easily model the relationship between the position of an object and its velocity, or its velocity and its acceleration.
Calculus is made up of two main concepts, differentiation and integration. Differentiation is the act of finding the rate of change of a given function (position of an object --> velocity of that object). Integration focuses on finding the original function given a function that models its rate of change (velocity of an object --> position of an object). As you can see these two operations are opposite, this relationship is defined in the fundamental theorem of calculus.
Foundational Concepts
Differentiation
Differentiation is the act of finding the rate of change of a given function, the resulting function is then referred to as the derivative. It uses its own notation.
If trying to find the derivative of a function of multiple variables then partial derivatives are used. Partial derivatives are a component of multivariable calculus.
Equations that include one or more derivatives are referred to as differential equations and are commonly used to model real world systems. Examples include disease infection in a population, two chemicals being mixed in a tank, heat transfer in a system, etc.
Integration
Integration finds the original function that produced the derivative, hence the integral of a function often being referred to as the anti-derivative. It is worth noting that the finding the integral of a function is the same as finding the area under the line plotted by that function and the y-axis. Integration uses its own notation.
If trying to find the integral of a function of multiple variables then multiple integrals are used. Multiple Integrals are a component of multivariable calculus.
Applications
Calculus can be used to find the geometric center of a shape, often called the centroid.
Related Topics
- See the following for further reading.