Definition

Noun: - The branch of mathematics concerned with limits and with the differentiation and integration of functions. It is the mathematical study of continuous change, encompassing two major complementary operations: differentiation (finding rates of change or slopes) and integration (finding areas under curves or accumulated quantities).

Usage

• Infinitesimal calculus is the formal term for the field commonly known simply as calculus. It is used in academic and formal contexts to refer to the foundational mathematical discipline.
• It is typically used as a singular, uncountable noun (e.g., ).

Examples

Advanced Usage

• The term infinitesimal calculus explicitly references the historical concept of "infinitesimals"—infinitely small quantities used in early formulations of the subject. Modern calculus is primarily based on the limit concept.
• It can be used to distinguish the classical continuous calculus from other branches like discrete calculus or calculus of variations.

Variants and Related Words

• Calculus: The common, shortened form of "infinitesimal calculus."
• Differential calculus: The subfield focusing on derivatives and rates of change.
• Integral calculus: The subfield focusing on integrals and accumulation.
• Analysis: Often used synonymously in higher mathematics, though it can refer to a broader set of theories.

Synonyms

• Calculus
• Mathematical analysis (in a broad sense)

Related Phrases

• Fundamental theorem of calculus: The central theorem linking differentiation and integration.
• Do calculus: A term used in applied fields, meaning to perform calculations using the methods of calculus (e.g., ).

Noun

1. the branch of mathematics that is concerned with limits and with the differentiation and integration of functions