Calculus: meaning, definitions and examples

General usage referring to the entire field of study that deals with rates of change and accumulation of quantities.

• Calculus is a required course for engineering students.
• She excelled in her calculus class and decided to major in mathematics.

Broader context encompassing calculus as well as other areas of advanced mathematics that deal with functions, limits, and infinity.

• Mathematical analysis provides the rigorous foundation for understanding calculus concepts.
• He published several papers on topics in mathematical analysis during his career.

Specific context of calculus focused on the concept of the derivative, rates of change, and slopes of curves.

• Differential calculus is used to find the slope of a tangent line to a curve at any point.
• The concept of limits is fundamental to understanding differential calculus.

Specific context of calculus that deals with the concept of the integral, accumulation of quantities, and areas under or between curves.

• Integral calculus is crucial for computing the area under a curve.
• In physics, integral calculus is often used to determine the total work done by a force over a distance.