infinitesimal calculus
Học thuậtThân thiện
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
- the branch of mathematics that is concerned with limits and with the differentiation and integration of functions