"Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations."
The study of limits, derivatives, integrals, and their applications to functions and equations.
Functions: A function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output.
Limits: A limit is the value that a function approaches as the input gets closer to a specific value.
Derivatives: The derivative of a function is the rate at which the function is changing at any given point.
Applications of Derivatives: Finding maximum and minimum values, optimization problems, determining concavity and inflection points, etc.
Integrals: An integral is a mathematical concept that describes the accumulation of a particular quantity over an interval of time or space.
Applications of Integrals: Finding areas, volumes, work done, etc.
Differential Equations: A differential equation is a mathematical equation that relates some function with its derivatives.
Series: A series is the sum of terms in an infinite sequence.
Power Series: A power series is a series that can be represented as an infinite polynomial.
Taylor Series: A Taylor series is a representation of a function as an infinite sum of terms.
"It has two major branches, differential calculus and integral calculus..."
"The former concerns instantaneous rates of change, and the slopes of curves..."
"The latter concerns accumulation of quantities, and areas under or between curves."
"These two branches are related to each other by the fundamental theorem of calculus..."
"They make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit."
"Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz."
"Later work, including codifying the idea of limits, put these developments on a more solid conceptual footing."
"Today, calculus has widespread uses in science, engineering, and social science."
"...geometry is the study of shape..."
"The former concerns instantaneous rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves."
"These two branches are related to each other by the fundamental theorem of calculus..."
"Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz."
"They make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit."
"Later work, including codifying the idea of limits, put these developments on a more solid conceptual footing."
"Today, calculus has widespread uses in science, engineering, and social science."
"It has two major branches, differential calculus and integral calculus..."
"The former concerns instantaneous rates of change, and the slopes of curves..."
"The latter concerns accumulation of quantities, and areas under or between curves."
"These two branches are related to each other by the fundamental theorem of calculus..."